Question

1. find all missing angles for the following (click for video #10):

Explanation:

Step1: Find angle 1

Adjacent angles on a straight line sum to \(180^{\circ}\). So, \(\angle1 = 180^{\circ}- 154^{\circ}\)

$$ \angle1=26^{\circ} $$

Step2: Find angle 2

Vertical angles are equal. So, \(\angle2 = 154^{\circ}\)

Step3: Find angle 3

Vertical angles are equal. So, \(\angle3=\angle1 = 26^{\circ}\)

Step4: Assume \(XY\parallel ZW\) (since no other info, common in such problems). Then \(\angle4=\angle1 = 26^{\circ}\) (alternate interior angles)

Step5: Find angle 5

\(\angle5 = 154^{\circ}\) (vertical angles with \(\angle2\))

Step6: Find angle 6

\(\angle6=\angle2 = 154^{\circ}\) (alternate interior angles if \(XY\parallel ZW\))

Step7: Find angle 7

\(\angle7=\angle3 = 26^{\circ}\) (alternate interior angles if \(XY\parallel ZW\))

Answer:

\(\angle1 = 26^{\circ}\), \(\angle2 = 154^{\circ}\), \(\angle3 = 26^{\circ}\), \(\angle4 = 26^{\circ}\), \(\angle5 = 154^{\circ}\), \(\angle6 = 154^{\circ}\), \(\angle7 = 26^{\circ}\)