Question

given: a||b and <6 = 37°
find: all remaining angles (4 pts).
(provide all theorems / reasoning and show all work**
<1 =
<2 =
<3 =
<4 =
<5 =
<7 =
<8 =

Explanation:

Step1: Find \(\angle 7\)

Vertical angles are equal. Since \(\angle 6 = 37^{\circ}\), and \(\angle 6\) and \(\angle 7\) are vertical angles, so \(\angle 7=37^{\circ}\)

Step2: Find \(\angle 5\)

\(\angle 5\) and \(\angle 6\) are supplementary (linear - pair). So \(\angle 5 = 180^{\circ}-\angle 6=180 - 37=143^{\circ}\)

Step3: Find \(\angle 8\)

\(\angle 8\) and \(\angle 5\) are vertical angles. So \(\angle 8=\angle 5 = 143^{\circ}\)

Step4: Find \(\angle 3\)

Since \(a\parallel b\), \(\angle 3\) and \(\angle 6\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(\angle 3 = 37^{\circ}\)

Step5: Find \(\angle 1\)

\(\angle 1\) and \(\angle 3\) are vertical angles. So \(\angle 1=\angle 3 = 37^{\circ}\)

Step6: Find \(\angle 2\)

\(\angle 2\) and \(\angle 1\) are supplementary (linear - pair). So \(\angle 2=180^{\circ}-\angle 1 = 180 - 37=143^{\circ}\)

Step7: Find \(\angle 4\)

\(\angle 4\) and \(\angle 2\) are vertical angles. So \(\angle 4=\angle 2=143^{\circ}\)

Answer:

\(\angle 1 = 37^{\circ}\), \(\angle 2 = 143^{\circ}\), \(\angle 3 = 37^{\circ}\), \(\angle 4 = 143^{\circ}\), \(\angle 5 = 143^{\circ}\), \(\angle 7 = 37^{\circ}\), \(\angle 8 = 143^{\circ}\)