Question

use the diagram and the given angle measure to find the other three angle measures.
$m\angle1 = 143^circ$
$m\angle2 = square^circ$
$m\angle3 = square^circ$
$m\angle4 = square^circ$

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)).
\(m\angle2=180^{\circ}-m\angle1\)
Substitute \(m\angle1 = 143^{\circ}\):
\(m\angle2=180^{\circ}- 143^{\circ}=37^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary (\(\angle2+\angle3 = 180^{\circ}\)).
\(m\angle3=180^{\circ}-m\angle2\)
Substitute \(m\angle2 = 37^{\circ}\):
\(m\angle3=180^{\circ}-37^{\circ}=143^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle1\) and \(\angle4\) are vertical angles (vertical angles are equal).
\(m\angle4=m\angle2 = 37^{\circ}\)

Answer:

\(m\angle2 = 37^{\circ}\), \(m\angle3 = 143^{\circ}\), \(m\angle4 = 37^{\circ}\)