Question a-circ
A circle has center , and points and lie on the circle. In triangle , the measure of is . What is the measure of , in degrees? (Disregard the degree symbol when entering your answer.)
A circle has center O , and points R and S lie on the circle. In
Hard-difficulty · SAT Math · Lines, Angles, and Triangles — Triangle sum theorem. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
The correct answer is . It's given that is the center of a circle and that points and lie on the circle. Therefore, and are radii of the circle. It follows that . If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles and , which are across from the sides of equal length, are congruent. Let represent the measure of . It follows that the measure of is also . It's given that the measure of is . Because the sum of the measures of the interior angles of a triangle is , the equation , or , can be used to find the measure of . Subtracting from both sides of this equation yields . Dividing both sides of this equation by yields . Therefore, the measure of , in degrees, is .
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