Question

1. woodworking oliver makes plaques like the one shown. find m∠1, m∠2, and m∠3, so he can cut the pieces of the plaque.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and the given $67^{\circ}$ angle are vertical angles. So $m\angle1 = 67^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. A linear pair of angles is supplementary, meaning the sum of their measures is $180^{\circ}$. So $m\angle2=180 - m\angle1$. Substituting $m\angle1 = 67^{\circ}$, we get $m\angle2=180 - 67=113^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. Since vertical angles are equal, $m\angle3 = m\angle2=113^{\circ}$.

Answer:

$m\angle1 = 67^{\circ}$, $m\angle2 = 113^{\circ}$, $m\angle3 = 113^{\circ}$