Question

1. in the figure to the right, $overline{ab}paralleloverline{cd}$ and $angle fjkcongangle fkj$, find $mangle ikd$.

Explanation:

Step1: Find the measure of $\angle FJK$

Since $\angle AHJ = 145^{\circ}$ and $\angle AHJ$ and $\angle FJK$ are vertical - angles, vertical angles are congruent. So $\angle FJK=\angle AHJ = 145^{\circ}$.

Step2: Use the given congruence

Given that $\angle FJK\cong\angle FKJ$, then $\angle FKJ = 145^{\circ}$.

Step3: Find the measure of $\angle IKD$

$\angle FKJ$ and $\angle IKD$ are vertical - angles. Since vertical angles are congruent, $m\angle IKD=m\angle FKJ$. So $m\angle IKD = 145^{\circ}$.

Answer:

$145^{\circ}$