Question

look at this diagram: if (overleftrightarrow{fh}) and (overleftrightarrow{ik}) are parallel lines and (mangle hgj = 117^{circ}), what is (mangle klj)? save answer

Explanation:

Step1: Identify angle - relationship

$\angle HGJ$ and $\angle KJL$ are vertical angles. Vertical angles are equal. So $m\angle KJL=m\angle HGJ = 117^{\circ}$.

Step2: Use linear - pair property

$\angle KJL$ and $\angle KJL$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. Let $m\angle KJL = x$ and $m\angle KJL=y$, then $x + y=180^{\circ}$. We know $x = 117^{\circ}$, so $y=180^{\circ}-117^{\circ}$.

Step3: Calculate the angle measure

$m\angle KJL=180 - 117=63^{\circ}$.

Answer:

$63$