A circle has center O , and points R and S lie on the circle. In triangle O R S

Question

A circle has center O , and points R and S lie on the circle. In triangle O R S , the measure of &#8736; R O S is 88 &#176; . What is the measure of &#8736; R S O , in degrees? (Disregard the degree symbol when entering your answer.)

Accepted Answer

The correct answer is 46 . It's given that O is the center of a circle and that points R and S lie on the circle. Therefore, O R /mo> and O S /mo> are radii of the circle. It follows that O R = O S . If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles R S O and O R S , which are across from the sides of equal length, are congruent. Let x /mo> represent the measure of R S O . It follows that the measure of O R S is also x /mo> . It's given that the measure of R O S is 88 /mo> . Because the sum of the measures of the interior angles of a triangle is 180 /mo> , the equation x /mo> + x /mo> + 88 /mo> = 180 /mo> , or 2 x + 88 = 180 , can be used to find the measure of R S O . Subtracting 88 from both sides of this equation yields 2 x = 92 . Dividing both sides of this equation by 2 yields x = 46 . Therefore, the measure of R S O , in degrees, is 46 .

Question 437a15