Question

1. if ( mangle3 = 54^{circ} ), find the measure of each missing angle.

( mangle9= )

Explanation:

Step1: Use the property of linear - pair angles

Angles that form a linear pair are supplementary, i.e., their sum is \(180^{\circ}\). \(\angle3\) and \(\angle5\) form a linear pair. So, \(m\angle3 + m\angle5=180^{\circ}\). Given \(m\angle3 = 54^{\circ}\), then \(m\angle5=180^{\circ}-m\angle3\).

Step2: Calculate \(m\angle5\)

Substitute \(m\angle3 = 54^{\circ}\) into the formula \(m\angle5 = 180^{\circ}-54^{\circ}=126^{\circ}\). \(\angle5\) and \(\angle9\) are vertical angles. Vertical angles are equal. So, \(m\angle9=m\angle5\).

Answer:

\(126^{\circ}\)