What is the measure of the exterior angle, x

Question

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32 degress and 37 degress

Please show work

Answer 1

To find the measure of the exterior angle (∠x), you need to know a fundamental rule about the angles of a triangle: the sum of the measures of the interior angles of a triangle is always 180 degrees.

Given two interior angles of a triangle are 32 degrees and 37 degrees, we can find the measure of the third interior angle by subtracting the sum of these two from 180 degrees:

180 degrees - (32 degrees + 37 degrees) = 180 degrees - 69 degrees = 111 degrees

So, the third interior angle measures 111 degrees.

Now, the exterior angle (∠x) of a triangle is equal to the sum of the two non-adjacent interior angles, which in this case are the ones that measure 32 degrees and 37 degrees.

∠x = 32 degrees + 37 degrees = 69 degrees

Therefore, the measure of the exterior angle, x, is 69 degrees.