Question

look at this diagram:

diagram showing two parallel horizontal lines fh and ik, and a transversal el intersecting them at g and j respectively

if \\( \overleftrightarrow{fh} \\) and \\( \overleftrightarrow{ik} \\) are parallel lines and \\( m\angle fgj = 110^\circ \\), what is \\( m\angle fge \\)?

blank box\\( ^\circ \\)

submit

Explanation:

Step1: Identify angle relationship

$\angle FGJ$ and $\angle FGE$ are supplementary angles (they form a linear pair), so their measures add up to $180^\circ$.

Step2: Calculate $m\angle FGE$

Let $m\angle FGE = x$. Then $x + m\angle FGJ = 180^\circ$. We know $m\angle FGJ = 110^\circ$, so $x + 110^\circ = 180^\circ$. Solving for $x$, we get $x = 180^\circ - 110^\circ = 70^\circ$.

Answer:

$70$