Question

use the diagram and the given angle measure to find the other three measures.
$m\angle3 = 159^{\circ}$
$m\angle1 = \square^{\circ}$
$m\angle2 = \square^{\circ}$
$m\angle4 = \square^{\circ}$

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle3\) are supplementary angles.
\(m\angle1 + m\angle3=180^{\circ}\)
\(m\angle1=180^{\circ}-m\angle3\)
Substitute \(m\angle3 = 159^{\circ}\)
\(m\angle1=180^{\circ}- 159^{\circ}=21^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles.
\(m\angle1 + m\angle2=180^{\circ}\)
\(m\angle2=180^{\circ}-m\angle1\)
Substitute \(m\angle1 = 21^{\circ}\)
\(m\angle2=180^{\circ}-21^{\circ}=159^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle3\) and \(\angle4\) are supplementary angles.
\(m\angle3 + m\angle4=180^{\circ}\)
\(m\angle4=180^{\circ}-m\angle3\)
Substitute \(m\angle3 = 159^{\circ}\)
\(m\angle4=180^{\circ}-159^{\circ}=21^{\circ}\)

Answer:

\(m\angle1 = 21^{\circ}\), \(m\angle2 = 159^{\circ}\), \(m\angle4 = 21^{\circ}\)