OG详解-OG3 数学2 Q13

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 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° +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.