In ▵RST, the measure of ∠R is 63°. Which of the following could be the measure, in degrees, of ∠S ?

Question

Accepted Answer

Choice A is correct. The sum of the measures of the angles of a triangle is 180°. Therefore, the sum of the measures of ∠R, ∠S, and ∠T is 180°. It’s given that the measure of ∠R is 63°. It follows that the sum of the measures of ∠S and ∠T is 180° − 63°, or 117°. Therefore, the measure of ∠S, in degrees, must be less than 117. Of the given choices, only 116 is less than 117. Thus, the measure, in degrees, of ∠S could be 116. Choice B is incorrect. If the measure of ∠S is 118°, then the sum of the measures of the angles of the triangle is greater than, not equal to, 180°. Choice C is incorrect. If the measure of ∠S is 126°, then the sum of the measures of the angles of the triangle is greater than, not equal to, 180°. Choice D is incorrect. This is the sum of the measures of the angles of a triangle, in degrees.

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