Question

1. in and ( m angle i=108^{circ} ) in the figure to the right, find the measures of ( angle a, angle c ), and ( angle h )( m angle a=) (type an integer or a decimal.)( m angle c=) (type an integer or a decimal.)

Explanation:

Step1: Find \(m\angle A\)

Since \(\angle A\) and \(\angle G\) are vertical angles. Vertical angles are equal. So \(m\angle A=m\angle G = 108^{\circ}\)

Step2: Find \(m\angle C\)

\(\angle A\) and \(\angle C\) are supplementary angles (they form a linear - pair). The sum of supplementary angles is \(180^{\circ}\). So \(m\angle C=180 - m\angle A\)
Substitute \(m\angle A = 108^{\circ}\) into the formula: \(m\angle C=180 - 108=72^{\circ}\)

Answer:

\(m\angle A = 108^{\circ}\), \(m\angle C = 72^{\circ}\)