Question

1. if (mangle6 = 72^{circ}), then (mangle7=?) a. (72^{circ}) b. (80^{circ}) c. (100^{circ}) d. (108^{circ})

Explanation:

Step1: Identify angle - relationship

$\angle6$ and $\angle7$ are a linear - pair of angles.

Step2: Recall linear - pair property

The sum of the measures of a linear - pair of angles is $180^{\circ}$. So, $m\angle6 + m\angle7=180^{\circ}$.

Step3: Solve for $m\angle7$

Given $m\angle6 = 72^{\circ}$, then $m\angle7=180^{\circ}-m\angle6$. Substitute $m\angle6 = 72^{\circ}$ into the equation: $m\angle7 = 180^{\circ}-72^{\circ}=108^{\circ}$.

Answer:

D. $108^{\circ}$