What is the measure of the exterior angle, x
?
32 degress and 37 degress
Please show work
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.