Question

look at this diagram:

diagram of parallel lines df and gi, and transversal jc intersecting them at e and h, with points g, i on gi; d, f on df; j, h, e, c on jc

if \\( \overleftrightarrow{df} \\) and \\( \overleftrightarrow{gi} \\) are parallel lines and \\( m\angle deh = 116.7^\circ \\), what is \\( m\angle ihe \\)?

blank box\\( ^\circ \\)

submit

Explanation:

Step1: Identify consecutive interior angles

$\overleftrightarrow{DF} \parallel \overleftrightarrow{GI}$, transversal $\overleftrightarrow{JC}$ creates consecutive interior angles $\angle DEH$ and $\angle IHE$. These angles are supplementary.

Step2: Calculate $\angle IHE$

Use supplementary angle sum: $m\angle IHE = 180^\circ - m\angle DEH$
Substitute value: $m\angle IHE = 180^\circ - 116.7^\circ$

Answer:

$63.3^\circ$