Question

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

Explanation:

Step1: Find angle 2

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

Step2: Find angle 3

If \(m\parallel n\) and \(q\parallel p\), angle 2 and angle 3 are same - side interior angles. For parallel lines \(m\parallel n\) and transversal \(p\), same - side interior angles are supplementary (\(\angle2+\angle3 = 180^{\circ}\))
\(\angle3=180^{\circ}-\angle2\)
Substitute \(\angle2 = 110^{\circ}\), \(\angle3=180 - 110=70^{\circ}\)

Step3: Find angle 4

If \(m\parallel n\) and \(q\parallel p\), angle 1 and angle 4 are same - side interior angles. For parallel lines \(q\parallel p\) and transversal \(m\), same - side interior angles are supplementary (\(\angle1+\angle4 = 180^{\circ}\))
\(\angle4=180^{\circ}-\angle1\)
Substitute \(\angle1 = 110^{\circ}\), \(\angle4=180 - 110=70^{\circ}\)

Answer:

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