Chapter 12.2, Problem 6C

To determine

To measure: $m\angle 1$ , $m\angle 2$ , $m\angle 3$ , $m\angle 4$ , $m\angle 5$ , $m\angle 7$ , $m\angle 8$

Answer to Problem 6C

Yes, we can measure all other angles.

Explanation of Solution

Given information : one angle is $m\angle 6$ .

Concept used : If two parallel lines are intersected by a transversal line then the corresponding angles are equal, alternate interior angles and alternate exterior angles are equal. Vertically opposite angles are equal. Sum consecutive interior angles are ${180}^{\circ }$ . Sum of linear pair angles are ${180}^{\circ }$ .

  $\begin{array}{l}m\angle 6+m\angle 5={180}^{\circ }\\ \Rightarrow m\angle 5={180}^{\circ }-m\angle 6\end{array}$

  $m\angle 6=m\angle 7$ (Vertically opposite angles)

  $m\angle 5=m\angle 8$ (Vertically opposite angles)

  $m\angle 5=m\angle 1$ (Corresponding angles)

  $m\angle 7=m\angle 3$ (Corresponding angles)

  $m\angle 6=m\angle 2$ (Corresponding angles)

  $m\angle 8=m\angle 4$ (Corresponding angles)