Question

look at this diagram: if $overleftrightarrow{gi}$ and $overleftrightarrow{jl}$ are parallel lines and $mangle ihk = 40^circ$, what is $mangle ihf$?

Explanation:

Step1: Identify angle relationship

Since \( \overleftrightarrow{GI} \parallel \overleftrightarrow{JL} \) and the transversal is the line through \( H \) and \( K \), \( \angle IHK \) and \( \angle IHF \) are supplementary (they form a linear pair, so their measures add up to \( 180^\circ \)).

Step2: Calculate \( m\angle IHF \)

We know \( m\angle IHK = 40^\circ \). Using the supplementary angle formula \( m\angle IHF + m\angle IHK = 180^\circ \), we solve for \( m\angle IHF \):
\( m\angle IHF = 180^\circ - m\angle IHK \)
\( m\angle IHF = 180^\circ - 40^\circ = 140^\circ \)

Answer:

\( 140 \)