Question

in parallelogram fghj if ( mangle fgh = 110^{circ} ) find ( mangle hjf ).

Explanation:

Step1: Use property of parallelogram

In a parallelogram, consecutive angles are supplementary. So \(m\angle FGH + m\angle GHJ= 180^{\circ}\). Given \(m\angle FGH = 110^{\circ}\), then \(m\angle GHJ=180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Use property of parallelogram (alternate - interior angles)

Since \(FG\parallel HJ\) and \(GH\parallel FJ\) in parallelogram \(FGHJ\), \(\angle HJF\) and \(\angle GHJ\) are alternate - interior angles. Alternate - interior angles formed by parallel lines are equal.

Answer:

\(70^{\circ}\)