OG详解-OG8 数学2 Q20

 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 xc. 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°+ 88 = 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.