Question

if angle 1 is 110°, what would the other angle measures have to be in order for m || n and q || p? angle 2 = 70° angle 3 = 110° angle 4 = 70°

Explanation:

Step1: Find angle 2

Angle 1 and angle 2 are supplementary angles (they form a linear pair). So, angle 2 = \(180^{\circ}-110^{\circ}=70^{\circ}\)

Step2: Find angle 3

Angle 3 and angle 1 are alternate - interior angles. When \(m\parallel n\) and \(q\parallel p\), alternate - interior angles are equal. So, angle 3 = \(110^{\circ}\)

Step3: Find angle 4

Angle 4 and angle 2 are corresponding angles. When \(m\parallel n\) and \(q\parallel p\), corresponding angles are equal. So, angle 4 = \(70^{\circ}\)

Answer:

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