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: Use vertical angles property

Vertical angles are equal. So \(m\angle1 = m\angle2\) and \(m\angle3 = m\angle4\). Given \(m\angle1=104^{\circ}\), then \(m\angle2 = 104^{\circ}\).

Step2: Use linear - pair property

Angles in a linear pair are supplementary (\(m\angle1+m\angle3 = 180^{\circ}\)). Since \(m\angle1 = 104^{\circ}\), then \(m\angle3=180^{\circ}-104^{\circ}=76^{\circ}\).

Step3: Use vertical angles property again

Since \(m\angle3 = 76^{\circ}\), and \(m\angle3 = m\angle4\) (vertical angles), so \(m\angle4 = 76^{\circ}\).

Answer:

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