Question

1. if angle 6 measures 106 what is the measure of angle 7a 106b 74c 90d 1802 if angle 6 measures 106 what is the measure of angle 1a 106b 74c 90d 1803 what is the vertical angle of angle 44 what is the vertical angle of angle 75 are angles 1 and 3 congruent to each other6 are angles 2 and 7 congruent to each other 7 lines a and b are: parallel or perpendicular?8 line t is a parallel line or a transversal?

Answer 1

(1) Angle 6 and angle 7 lie on a straight line. Therefore

`\begin{gathered} \angle6+\angle7=180\text{ (angles on a straight line sum up to 180)} \\ 106+\angle7=180 \\ \angle7=180-106 \\ \angle7=74 \end{gathered}`

(2) If angle 6 equals 106, then angle 4 corresponds to angle 6. Therefore angle 4 equals 106. Angle 1 and angle 4 lie on a straight line. Therefore;

`\begin{gathered} \angle1+\angle4=180 \\ \angle1+106=180 \\ \angle1=180-106 \\ \angle1=74 \end{gathered}`

(3) Angle 3 is vertically opposite to angle 4

(4) Angle 8 is vertically opposite to angle 7

(5) Angles 1 and 3 are NOT CONGRUENT to each other

(6) Angles 2 and 7 are CONGRUENT to each other. Interior alternate angles are equal. Angles 2 and 7 are interior alternate angles

(7) Lines a and b are PARALLEL

(8) Line t is a TRANSVERSAL