Question

for the figure shown, find m∠1 and m∠2. m∠1 = 129°. m∠2 = □°

Explanation:

Step1: Use exterior - angle property of a triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's assume the non - adjacent interior angles to $\angle1$ are $x$ and $y$. We know that $\angle1$ is an exterior angle of the triangle. If we assume the interior angles of the triangle are related to the given angles in the figure. Let's say the two non - adjacent interior angles to $\angle1$ are $46^{\circ}$ and $30^{\circ}+ \angle2$. So, $m\angle1=46^{\circ}+(30^{\circ}+m\angle2)$.

Step2: Substitute the value of $m\angle1$

Given $m\angle1 = 129^{\circ}$, we substitute it into the equation $129^{\circ}=46^{\circ}+30^{\circ}+m\angle2$.

Step3: Solve for $m\angle2$

First, simplify the right - hand side: $46^{\circ}+30^{\circ}=76^{\circ}$. Then the equation becomes $129^{\circ}=76^{\circ}+m\angle2$. Subtract $76^{\circ}$ from both sides: $m\angle2=129^{\circ}-76^{\circ}$. So, $m\angle2 = 53^{\circ}$.

Answer:

$53$