Question

this problem illustrates that a circumscribed angle and its associated central angle are supplementary.
examine the diagram.
circumscribed angle gls intercepts circle a at points g and s.
central angle gas also intercepts circle a at points g and s.
if ∠gls measures 82°, what is the measure of ∠gas?
use the keypad to enter your answer in the box. include the symbol for the units of measure.

Explanation:

Step1: Recall the property of circumscribed and central angles

A circumscribed angle and its associated central angle are supplementary. That is, if the circumscribed angle is \(\angle GLS\) and the central angle is \(\angle GAS\), then \(\angle GLS+\angle GAS = 180^{\circ}\).

Step2: Solve for \(\angle GAS\)

Given \(\angle GLS = 82^{\circ}\), we substitute into the equation \(\angle GAS=180^{\circ}-\angle GLS\).

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Answer:

\(98^{\circ}\)