Question

look at this diagram: if (overrightarrow{fh}) and (overrightarrow{ik}) are parallel lines and (mangle ijg = 66^{circ}), what is (mangle kjg?)

Explanation:

Step1: Identify angle - relationship

$\angle IJG$ and $\angle KJG$ are a linear - pair of angles.

Step2: Recall linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. So $m\angle IJG + m\angle KJG=180^{\circ}$.

Step3: Solve for $m\angle KJG$

Given $m\angle IJG = 66^{\circ}$, then $m\angle KJG=180^{\circ}-m\angle IJG$. Substitute $m\angle IJG = 66^{\circ}$ into the equation: $m\angle KJG = 180 - 66=114^{\circ}$.

Answer:

$114$