In the diagram below, two lines tangent to a circle from an external point form an...

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Problem

In the diagram below, two lines tangent to a circle from an external point form an angle. The arc intercepted by the angle is given. Find the measure of the major arc.

Step-by-step solution

The angle formed by the tangents is $72^\circ$. The measure of the intercepted minor arc ADC is $360^\circ - 2 \times 72^\circ = 216^\circ$. The measure of arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of arc ADC is $360^\circ - 108^\circ = 252^\circ$. Wait, the question asks for arc ADC. The angle $108^\circ$ is the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. However, the diagram shows $108^\circ$ as the arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc AC is $180^\circ - 72^\circ = 108^\circ$. The measure of the major arc ADC is $360^\circ - 108^\circ = 252^\circ$. The diagram shows $108^\circ$ as the measure of arc AC. The angle formed by the tangents is $72^\circ$. The sum of the angle formed by the tangents and the intercepted minor arc is $180^\circ$. So, the minor arc

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216