Question

look at this diagram: if $overleftrightarrow{gi}$ and $overleftrightarrow{jl}$ are parallel lines and $mangle{jkh}=120.7^{circ}$, what is $mangle{ihk}$?

Explanation:

Step1: Identify angle - relationship

$\angle{JKH}$ and $\angle{IHK}$ are supplementary angles since $\overleftrightarrow{GI}$ and $\overleftrightarrow{JL}$ are parallel lines and they are same - side interior angles.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle{IHK}=x$. Then $m\angle{JKH}+x = 180^{\circ}$. Given $m\angle{JKH}=120.7^{\circ}$, we have $x=180^{\circ}- 120.7^{\circ}$.

Step3: Calculate the angle measure

$x = 180 - 120.7=59.3^{\circ}$

Answer:

$59.3$