Question

name the two pairs of vertical angles in the figure.
∠1 and ∠3
∠2 and ∠4

m∠1 = 104°. find the remaining three angle measures.
m∠2 =
m∠3 = ?
m∠4 = ?

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles.
\(m\angle1 + m\angle2=180^{\circ}\)
\(104^{\circ}+m\angle2 = 180^{\circ}\)
\(m\angle2=180^{\circ}- 104^{\circ}=76^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary angles.
\(m\angle2 + m\angle3=180^{\circ}\)
\(76^{\circ}+m\angle3 = 180^{\circ}\)
\(m\angle3=180^{\circ}-76^{\circ}=104^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle1\) and \(\angle4\) are vertical angles.
Vertical angles are equal.
\(m\angle4=m\angle1 = 104^{\circ}\)

Answer:

\(m\angle2 = 76^{\circ}\)
\(m\angle3 = 104^{\circ}\)
\(m\angle4 = 104^{\circ}\)