Question

use the triangle shown. if $mangle2 = 23^{circ}$ and $mangle3 = 68^{circ}$, what is $mangle1$? a. $23^{circ}$ b. $68^{circ}$ c. $89^{circ}$ d. $91^{circ}$

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, $\angle1$ is an exterior angle and $\angle2$ and $\angle3$ are the non - adjacent interior angles.

Step2: Calculate $m\angle1$

$m\angle1=m\angle2 + m\angle3$. Substitute $m\angle2 = 23^{\circ}$ and $m\angle3=68^{\circ}$ into the formula. So, $m\angle1=23^{\circ}+68^{\circ}=91^{\circ}$.

Answer:

D. $91^{\circ}$