Question

air hockey when an air hockey puck is hit into the sideboards, it bounces off so that ∠1 and ∠2 are congruent. find m∠1, m∠2, m∠3, and m∠4. 52. 106° 1 3 2 4

Explanation:

Step1: Find $m\angle1$

Since a straight - line is $180^{\circ}$, and one angle adjacent to $\angle1$ is $106^{\circ}$, then $m\angle1=180 - 106=74^{\circ}$.

Step2: Use congruence to find $m\angle2$

Given that $\angle1$ and $\angle2$ are congruent, so $m\angle2 = m\angle1=74^{\circ}$.

Step3: Find $m\angle3$

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are congruent, so $m\angle3=m\angle1 = 74^{\circ}$.

Step4: Find $m\angle4$

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are congruent, so $m\angle4=m\angle2 = 74^{\circ}$.

Answer:

$m\angle1 = 74^{\circ}$, $m\angle2 = 74^{\circ}$, $m\angle3 = 74^{\circ}$, $m\angle4 = 74^{\circ}$