Question

1. given ( x | y ) and ( m angle 5=104^{circ} ) and ( m angle 9=81^{circ} ), find the following: ( m angle 2= ) ( m angle 13= )

Explanation:

Step1: Find \(m\angle2\)

Since \(x\parallel y\), \(\angle2\) and \(\angle9\) are corresponding angles.
By the Corresponding Angles Postulate, \(m\angle2 = m\angle9\).
Given \(m\angle9 = 81^{\circ}\), so \(m\angle2=81^{\circ}\).

Step2: Find \(m\angle13\)

Since \(x\parallel y\), \(\angle5\) and \(\angle13\) are same - side interior angles.
By the Same - Side Interior Angles Theorem, \(m\angle5+m\angle13 = 180^{\circ}\).
Given \(m\angle5 = 104^{\circ}\), then \(m\angle13=180^{\circ}-m\angle5\).
Substitute \(m\angle5 = 104^{\circ}\) into the formula: \(m\angle13=180 - 104=76^{\circ}\).

Answer:

\(m\angle2 = 81^{\circ}\), \(m\angle13 = 76^{\circ}\)