Question

use the diagram and the given angle measure to find the other three measures.

$m\angle2 = 34^{\circ}$

$m\angle1 = \square^{\circ}$

$m\angle3 = \square^{\circ}$

$m\angle4 = \square^{\circ}$

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary.
\(m\angle1 + m\angle2=180^{\circ}\)
\(m\angle1=180^{\circ}-m\angle2\)
Substitute \(m\angle2 = 34^{\circ}\)
\(m\angle1=180^{\circ}- 34^{\circ}=146^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles.
Vertical angles are equal.
So \(m\angle3=m\angle1 = 146^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle2\) and \(\angle4\) are vertical angles.
Vertical angles are equal.
So \(m\angle4=m\angle2=34^{\circ}\)

Answer:

\(m\angle1 = 146^{\circ}\)
\(m\angle3 = 146^{\circ}\)
\(m\angle4 = 34^{\circ}\)