Question

1. find the measure of each missing angle.

m∠1=
m∠2=
m∠3=
m∠4=

Explanation:

Step1: Find \(m\angle3\)

Use the linear - pair relationship. \(\angle3\) and \(93^{\circ}\) form a linear pair. So \(m\angle3 = 180^{\circ}-93^{\circ}=87^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle2\) and \(49^{\circ}\) are vertical angles. Vertical angles are equal. So \(m\angle2 = 49^{\circ}\)

Step3: Find \(m\angle1\)

In the left - hand triangle, use the triangle - angle sum theorem (\(m\angle1 + m\angle2+68^{\circ}=180^{\circ}\)). Substitute \(m\angle2 = 49^{\circ}\) into the equation: \(m\angle1=180^{\circ}-68^{\circ}-49^{\circ}=63^{\circ}\)

Step4: Find \(m\angle4\)

In the right - hand triangle, use the triangle - angle sum theorem (\(m\angle3 + 49^{\circ}+m\angle4=180^{\circ}\)). Substitute \(m\angle3 = 87^{\circ}\) into the equation: \(m\angle4=180^{\circ}-87^{\circ}-49^{\circ}=44^{\circ}\)

Answer:

\(m\angle1 = 63^{\circ}\), \(m\angle2 = 49^{\circ}\), \(m\angle3 = 87^{\circ}\), \(m\angle4 = 44^{\circ}\)