A quadrilateral is circumscribed about a circle. Two angles are given as 72 degrees...
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Problem
A quadrilateral is circumscribed about a circle. Two angles are given as 72 degrees and 3x degrees. Find the value of x.
Step-by-step solution
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, $\angle A + \angle C = 180^{\circ}$. Given $\angle A = 72^{\circ}$ and $\angle C = 3x^{\circ}$, we have $72^{\circ} + 3x^{\circ} = 180^{\circ}$. Solving for x: $3x = 180 - 72$, $3x = 108$, $x = 108 / 3 = 36$.
Answer
36