Question

look at this diagram: if \\( \overleftrightarrow { bd } \\) and \\( \overleftrightarrow { eg } \\) are parallel lines and \\( m \angle g f h = 57.3 ^ { \circ } \\), what is \\( m \angle b c a \\)?

Explanation:

Step1: Identify the relationship between angles

Since \(BD\parallel EG\), \(\angle GFH\) and \(\angle BCA\) are vertical angles (or use the property of parallel lines and transversal: alternate - interior angles are equal when two parallel lines are cut by a transversal. Here, \(\angle GFH\) and \(\angle BCA\) are congruent).

Step2: Determine the measure of \(\angle BCA\)

Given \(m\angle GFH = 57.3^{\circ}\), and because \(\angle BCA\cong\angle GFH\) (by the property of parallel lines and transversal or vertical - angle property in the context of parallel lines), so \(m\angle BCA=m\angle GFH\).

Answer:

\(57.3\)