Question
What is the measure of the exterior angle, x? Show your work. 32 and 37
Answers
GPT-4o mini
To find the measure of the exterior angle \( x \), we can make use of the fact that the exterior angle of a polygon is equal to the sum of the two remote interior angles that are not adjacent to it.
Given two interior angles measuring \( 32^\circ \) and \( 37^\circ \), we first calculate the sum of these two angles:
\[
32^\circ + 37^\circ = 69^\circ
\]
According to the exterior angle theorem:
\[
x = 180^\circ - \text{(sum of the two given interior angles)}
\]
Since the exterior angle is equal to the sum of the two other non-adjacent interior angles (in this case, it should be equal to \( 69^\circ \)):
\[
x = 69^\circ
\]
Thus, the measure of the exterior angle \( x \) is \( 69^\circ \).
Given two interior angles measuring \( 32^\circ \) and \( 37^\circ \), we first calculate the sum of these two angles:
\[
32^\circ + 37^\circ = 69^\circ
\]
According to the exterior angle theorem:
\[
x = 180^\circ - \text{(sum of the two given interior angles)}
\]
Since the exterior angle is equal to the sum of the two other non-adjacent interior angles (in this case, it should be equal to \( 69^\circ \)):
\[
x = 69^\circ
\]
Thus, the measure of the exterior angle \( x \) is \( 69^\circ \).