Question

40 name the two pairs of vertical angles in the figure. 40 ∠1 and ∠3 ∠2 and ∠4 m∠1 = 104°, find the remaining three angle measures. m∠2 = m∠3 = m∠4 =

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). \(\angle1\) and \(\angle2\) are supplementary.
\(m\angle1 + m\angle2=180^{\circ}\)
Since \(m\angle1 = 104^{\circ}\), then \(m\angle2=180^{\circ}- 104^{\circ}=76^{\circ}\)

Step2: Use the property of vertical angles

Vertical angles are equal. \(\angle1\) and \(\angle3\) are vertical angles. So \(m\angle3=m\angle1 = 104^{\circ}\)

Step3: Use the property of vertical angles

\(\angle2\) and \(\angle4\) are vertical angles. So \(m\angle4=m\angle2 = 76^{\circ}\)

Answer:

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