Question

look at this diagram: if \\( \overleftrightarrow { c e } \\) and \\( \overleftrightarrow { f h } \\) are parallel lines and \\( m \angle c d b = 113 ^ { \circ } \\), what is \\( m \angle f g i \\)?

Explanation:

Step1: Find the measure of the adjacent angle to ∠CDB

Since ∠CDB and ∠CDG form a linear - pair (they are adjacent and supplementary), and \(m\angle CDB = 113^{\circ}\).
We know that \(m\angle CDB+m\angle CDG = 180^{\circ}\).
So, \(m\angle CDG=180^{\circ}-113^{\circ}=67^{\circ}\).

Step2: Use the property of parallel lines and corresponding angles

Because \(CE\parallel FH\) and \(IB\) is a transversal.
\(\angle FGI\) and \(\angle CDG\) are corresponding angles.
When two parallel lines are cut by a transversal, corresponding angles are equal. So \(m\angle FGI=m\angle CDG\).

Answer:

\(67\)