Question

for the figure shown, find m∠1 and m∠2. (the figure is not drawn to scale.) m∠1 =

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the larger triangle, if we consider the exterior angle of measure $134^{\circ}$, we have $134^{\circ}=m\angle1 + 26^{\circ}$.
So, $m\angle1=134^{\circ}- 26^{\circ}$.

Step2: Calculate $m\angle1$

$m\angle1 = 108^{\circ}$.

Step3: Use angle - sum property of a triangle

In the smaller triangle, the sum of interior angles is $180^{\circ}$. One angle is $m\angle1 = 108^{\circ}$ and another is $18^{\circ}$. Let $m\angle2=x$. Then $180^{\circ}=108^{\circ}+18^{\circ}+x$.
So, $x=m\angle2=180^{\circ}-(108^{\circ}+18^{\circ})$.

Step4: Calculate $m\angle2$

$m\angle2 = 54^{\circ}$.

Answer:

$m\angle1 = 108^{\circ}$, $m\angle2 = 54^{\circ}$