Question

look at this diagram: if (overleftrightarrow{fh}) and (overleftrightarrow{ik}) are parallel lines and (mangle fgj = 132^{circ}), what is (mangle kjg?)

Explanation:

Step1: Identify angle - relationship

$\angle FGJ$ and $\angle KJG$ are alternate - interior angles. Since $\overleftrightarrow{FH}$ and $\overleftrightarrow{IK}$ are parallel lines, alternate - interior angles are congruent. So $m\angle KJG=m\angle FGJ = 132^{\circ}$.

Step2: Recognize linear - pair

$\angle KJG$ and $\angle KIG$ form a linear pair. The sum of the measures of angles in a linear pair is $180^{\circ}$. Let $m\angle KIG=x$. Then $x + m\angle KJG=180^{\circ}$.

Step3: Solve for $m\angle KIG$

Substitute $m\angle KJG = 132^{\circ}$ into the equation $x + m\angle KJG=180^{\circ}$. We get $x=180 - 132$. So $x = 48^{\circ}$.

Answer:

$48$