Question

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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 supplementary angles.
\(m\angle1 + m\angle4=180^{\circ}\)
\(104^{\circ}+m\angle4 = 180^{\circ}\)
\(m\angle4=180^{\circ}-104^{\circ}=76^{\circ}\)

Answer:

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