In △ R S T , the measure of ∠ R is 63 ° . Which of the following could

Question

In &#9651; R S T , the measure of &#8736; R is 63 &#176; . Which of the following could be the measure, in degrees, of &#8736; S ?

Accepted Answer

Choice A is correct. The sum of the measures of the angles of a triangle is 180 &#176; . Therefore, the sum of the measures of &#8736; R , &#8736; S , and &#8736; T is 180 &#176; . It's given that the measure of &#8736; R is 63 &#176; . It follows that the sum of the measures of &#8736; S and &#8736; T is 180 - 63 &#176; , or 117 &#176; . Therefore, the measure of &#8736; S , in degrees, must be less than 117 . Of the given choices, only 116 is less than 117 . Thus, the measure, in degrees, of &#8736; S could be 116 . Choice B is incorrect. If the measure of &#8736; S is 118 &#176; , then the sum of the measures of the angles of the triangle is greater than, not equal to, 180 &#176; . Choice C is incorrect. If the measure of &#8736; S is 126 &#176; , then the sum of the measures of the angles of the triangle is greater than, not equal to, 180 &#176; . Choice D is incorrect. This is the sum of the measures of the angles of a triangle, in degrees.

Question in-965