Question

use the diagram to find the measures of all the angles, given that ( mangle2 = 159^{circ}).( mangle1=square^{circ})( mangle3=square^{circ})( mangle4=square^{circ})

Explanation:

Step1: Find \(m\angle1\)

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

Step2: Find \(m\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles.
Vertical angles are equal.
So \(m\angle3=m\angle1 = 21^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle2\) and \(\angle4\) are vertical angles.
Vertical angles are equal.
So \(m\angle4=m\angle2 = 159^{\circ}\)

Answer:

\(m\angle1 = 21^{\circ}\)
\(m\angle3 = 21^{\circ}\)
\(m\angle4 = 159^{\circ}\)