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A circle has center O, and points R and S lie on the ORS ∠ROS 88° circle. In triangle, the measure of is. ∠RSO What is the measure of, in degrees? (Disregard the degree symbol when entering your answer.)
Correct answer: 46 (parsed from the explanation — this source omits an answer key for this item)
Explanation
46 The correct answer is . 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 c across from the sides of equal length, are congruent. Let x represent the + + c measure of RSO. It follows that the measure of ORS is also x . It’s given that + c the measure of ROS is 88. Because the sum of the measures of the interior 180c c+ c+88c=180c 2 +88=180 angles of a triangle is , the equation x x , or x , can + be used to find the measure of RSO. Subtracting 88 from both sides of this 2 =92 =46 equation yields x . Dividing both sides of this equation by 2 yields x . + 46 Therefore, the measure of RSO, in degrees, is .
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