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

Since \(m\parallel n\) and \(q\parallel p\), angle 1 and angle 2 are vertical angles. Vertical angles are equal.
\(\angle2 = 110^{\circ}\)

Step2: Find angle 3

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

Step3: Find angle 4

Angle 3 and angle 4 are vertical angles. Vertical angles are equal.
\(\angle4 = 70^{\circ}\)

Answer:

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