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 = 70°

Explanation:

Step1: Find Angle 2

Angle 1 and Angle 2 are vertical angles. Vertical angles are equal.
So, $\angle2=\angle1 = 110^{\circ}$

Step2: Find Angle 3

Since $m\parallel n$, Angle 2 and Angle 3 are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.
So, $\angle3=\angle2 = 110^{\circ}$

Step3: Find Angle 4

Since $q\parallel p$, Angle 1 and Angle 4 are same - side interior angles. Same - side interior angles are supplementary ($\angle1+\angle4 = 180^{\circ}$)
$\angle4=180^{\circ}-\angle1=180 - 110=70^{\circ}$ (already given)

Answer:

Angle 2 = $110^{\circ}$, Angle 3 = $110^{\circ}$