Question

7 the legs of the drafting table form vertical angles. find the measures of ∠1, ∠2 and ∠3. angle 85° 95° ∠1 ∠2 ∠3

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. $\angle1$ and the given $85^{\circ}$ angle are vertical angles. So, $\angle1 = 85^{\circ}$.

Step2: Recall linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So, $\angle2=180^{\circ}-\angle1 = 180 - 85=95^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. Since vertical angles are congruent, $\angle3=\angle2 = 95^{\circ}$.

Answer:

$\angle1 = 85^{\circ}$, $\angle2 = 95^{\circ}$, $\angle3 = 95^{\circ}$