Question #24cec8d1 - SAT Suite Question Bank

ID: 24cec8d1

Modded SAT Question Bank by Abdullah Mallik

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

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Correct Answer: 46

Rationale

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, $\bar{O R}$ and $\bar{O S}$ 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 $x °$ represent the measure of $∠ R S O$ . It follows that the measure of $∠ O R S$ is also $x °$ . It's given that the measure of $∠ R O S$ is $88 degree$ . Because the sum of the measures of the interior angles of a triangle is $180 degree$ , the equation $x ° + x ° + 88 ° = 180 °$ , 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 $2 x equals 92$ . Dividing both sides of this equation by $2$ yields $x equals 46$ . Therefore, the measure of $∠ R S O$ , in degrees, is $46$ .

Question Difficulty: Hard