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

In $△ X Y Z$ , the measure of $∠ X$ is $23 degree$ and the measure of $∠ Y$ is $66 degree$ . What is the measure of $∠ Z$ ?

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Explanation

Choice C is correct. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is $180 degree$ . It's given that in $△ X Y Z$ , the measure of $∠ X$ is $23 degree$ and the measure of $∠ Y$ is $66 degree$ . It follows that the measure of $∠ Z$ is $(180 - 23 - 66) °$ , or $91 degree$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the sum of the measures of $∠ X$ and $∠ Y$ , not the measure of $∠ Z$ .

Choice D is incorrect and may result from conceptual or calculation errors.