Question

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

Explanation:

Step1: Find angle 1

Use the concept of supplementary angles. Supplementary angles sum to \(180^{\circ}\).
\(\angle1 = 180^{\circ}- 110^{\circ}=70^{\circ}\)

Step2: Find angle 2

Use the concept of supplementary angles.
\(\angle2 = 180^{\circ}- 115^{\circ}=65^{\circ}\)

Step3: Find angle 3

\(\angle3\) and \(\angle2\) are vertical angles. Vertical angles are equal.
\(\angle3=\angle2 = 65^{\circ}\)

Step4: Find angle 4

\(\angle4\) and \(115^{\circ}\) are vertical angles. Vertical angles are equal.
\(\angle4 = 115^{\circ}\)

Step5: Find angle 6

\(\angle6\) and \(\angle1\) are vertical angles. Vertical angles are equal.
\(\angle6=\angle1 = 70^{\circ}\)

Step6: Find angle 7

Use the triangle - angle sum theorem (the sum of angles in a triangle is \(180^{\circ}\)). Let's assume the third angle in the triangle (not labeled) is \(x\). But we can also use the property of parallel lines (if we assume the two horizontal lines are parallel). \(\angle7\) and \(\angle3\) and \(\angle1\) can be related. Another way: \(\angle7\) and \(\angle6\) are supplementary (if we consider the line \(q\)). But using the property that \(\angle7\) and \(\angle3\) and \(\angle1\) in a triangle - like figure (assuming the lines are arranged such that we can use angle - sum). Also, \(\angle7 = 180^{\circ}-\angle1-\angle3\). Substitute \(\angle1 = 70^{\circ}\) and \(\angle3=65^{\circ}\).
\(\angle7=180^{\circ}-70^{\circ}-65^{\circ}=45^{\circ}\)

Answer:

Angle 1: \(70^{\circ}\), Angle 2: \(65^{\circ}\), Angle 3: \(65^{\circ}\), Angle 4: \(115^{\circ}\), Angle 6: \(70^{\circ}\), Angle 7: \(45^{\circ}\)