A circle has center O, and points R and S lie on the circle. In triangle ORS, the measure of ∠ROS is 88°. What is the measure of ∠RSO, in degrees?

Explanation

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, OR and OS are radii of the circle. It follows that OR = OS. If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles ∠ RSO and ∠ORS, which are across from the sides of equal length, are congruent. Let x° represent the measure of ∠ RSO. It follows that the measure of ∠ORS is also x°. It's given that the measure of ∠ ROS is 88°. Because the sum of the measures of the interior angles of a triangle is 180°, the equation x° + x° + 80°= 180° or 2x + 88 = 180, can be used to find the measure of ∠ RSO. Subtracting 88 from both sides of this equation yields 2x = 92. Dividing both sides of this equation by 2 yields x = 46. Therefore, the measure of ∠ RSO, in degrees, is 46.