Question

solving for unknown angle measures
if angle 1 is 110°, what would the other angle measures have to be in order for ( m parallel n ) and ( q parallel p )?
angle ( 2 = )
angle ( 3 = )
angle ( 4 = )

Explanation:

Step1: Find angle 2

Since angle 1 and angle 2 are vertical angles. Vertical angles are equal. So, angle 2 = angle 1.
Given angle 1 = \(110^{\circ}\), so angle 2=\(110^{\circ}\)

Step2: Find angle 3

Since \(m\parallel n\), angle 2 and angle 3 are same - side interior angles. For parallel lines \(m\) and \(n\) cut by a transversal, same - side interior angles are supplementary (\(\angle2+\angle3 = 180^{\circ}\)).
If \(\angle2 = 110^{\circ}\), then \(\angle3=180^{\circ}-\angle2\). Substitute \(\angle2 = 110^{\circ}\), we get \(\angle3 = 180 - 110=70^{\circ}\)

Step3: Find angle 4

Since \(q\parallel p\) and \(m\parallel n\), angle 4 and angle 3 are vertical angles. Vertical angles are equal. So, angle 4 = angle 3.
Since \(\angle3 = 70^{\circ}\), then \(\angle4 = 70^{\circ}\)

Answer:

Angle 2 = \(110^{\circ}\), Angle 3 = \(70^{\circ}\), Angle 4 = \(70^{\circ}\)