inscribed angle measure
Check the final answer first, then review the worked steps.
Problem
inscribed angle measure
Answer
\(79^{\circ}\)
Step-by-step solution
- Identify the geometric properties: The problem asks for the measure of the inscribed angle $\angle RST$ in a circle. We are given the measure of the intercepted arc $RT$, which is $158^{\circ}$.
- Apply the Inscribed Angle Theorem: The Inscribed Angle Theorem states that the measure of an inscribed angle is exactly half the measure of its intercepted arc. Mathematically, this is expressed as: $$\angle RST = \frac{1}{2} \times m(\text{arc } RT)$$
- Calculate the measure: Substitute the given value of the arc into the formula: $$\angle RST = \frac{1}{2} \times 158^{\circ}$$
- Perform the division: Dividing $158$ by $2$ gives: $$\angle RST = 79^{\circ}$$