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 = 104
m∠4 =?

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). For \(\angle1\) and \(\angle2\), we have \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1 = 104^{\circ}\), then \(m\angle2=180^{\circ}-m\angle1\).

$$m\angle2 = 180 - 104=76^{\circ}$$

Step2: Use the property of vertical angles

Vertical angles are equal. Since \(\angle1\) and \(\angle3\) are vertical angles (\(m\angle3 = 104^{\circ}\) as given, which is correct by vertical - angle property), and \(\angle2\) and \(\angle4\) are vertical angles. So \(m\angle4=m\angle2\)

$$m\angle4 = 76^{\circ}$$

Answer:

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