Question

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

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 triangle with $\angle1$, the exterior angle is $97^{\circ}$ and the two non - adjacent interior angles are $31^{\circ}$ and $\angle1$. So, $97^{\circ}=31^{\circ}+\angle1$.

Step2: Solve for $\angle1$

Subtract $31^{\circ}$ from both sides of the equation: $\angle1 = 97^{\circ}-31^{\circ}$.
$\angle1=66^{\circ}$

Answer:

$66$