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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

In $△ R S T$ , the measure of $∠ R$ is $63 degree$ . Which of the following could be the measure, in degrees, of $∠ S$ ?

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Explanation

Choice A is correct. The sum of the measures of the angles of a triangle is $180 degree$ . Therefore, the sum of the measures of $∠ R$ , $∠ S$ , and $∠ T$ is $180 degree$ . It's given that the measure of $∠ R$ is $63 degree$ . It follows that the sum of the measures of $∠ S$ and $∠ T$ is $left parenthesis 180 minus 63 right parenthesis degree$ , or $117 degree$ . 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 $118 degree$ , then the sum of the measures of the angles of the triangle is greater than, not equal to, $180 degree$ .

Choice C is incorrect. If the measure of $∠ S$ is $126 degree$ , then the sum of the measures of the angles of the triangle is greater than, not equal to, $180 degree$ .

Choice D is incorrect. This is the sum of the measures of the angles of a triangle, in degrees.