Question

1. if gi bisects ∠dip and m∠dig = 65°, what is m∠pig and m∠dip? explain!

Explanation:

Step1: Recall angle - bisector definition

By the definition of an angle - bisector, if a ray $GI$ bisects $\angle DIP$, then it divides $\angle DIP$ into two congruent angles. That is, $\angle DIG\cong\angle PIG$.

Step2: Find $m\angle PIG$

Since $\angle DIG\cong\angle PIG$ and $m\angle DIG = 65^{\circ}$, then $m\angle PIG=65^{\circ}$.

Step3: Find $m\angle DIP$

Since $\angle DIP=\angle DIG+\angle PIG$ and $\angle DIG = \angle PIG = 65^{\circ}$, then $m\angle DIP=m\angle DIG + m\angle PIG=65^{\circ}+65^{\circ}=130^{\circ}$.

Answer:

$m\angle PIG = 65^{\circ}$ and $m\angle DIP = 130^{\circ}$