Question

find the measures of angles 1 - 7
angle 1
angle 2
angle 3
angle 4

Explanation:

Step1: Find angle 1

Using the concept of linear - pair angles (sum of angles on a straight line is \(180^{\circ}\)).
If one angle is \(110^{\circ}\), then \(\angle1 = 180^{\circ}- 110^{\circ}=70^{\circ}\)

Step2: Find angle 2

Using the concept of linear - pair angles.
If one angle is \(115^{\circ}\), then \(\angle2=180^{\circ}-115^{\circ} = 65^{\circ}\)

Step3: Find angle 3

Since \(\angle2\) and \(\angle3\) are alternate interior angles (when two parallel lines \(q\) and \(m\) are cut by a transversal).
\(\angle3=\angle2 = 65^{\circ}\)

Step4: Find angle 4

Using the concept of linear - pair angles.
\(\angle4=180^{\circ}-\angle3=180^{\circ}-65^{\circ}=115^{\circ}\)

Answer:

\(\angle1 = 70^{\circ}\), \(\angle2 = 65^{\circ}\), \(\angle3 = 65^{\circ}\), \(\angle4 = 115^{\circ}\)