Chapter 5.1, Problem 1CE

a.

To determine

To state: the reason why $\angle G$ is supplementary to $\angle M$

Explanation of Solution

Given information: $GRAM$ is a parallelogram

  

As $GRAM$ is a parallelogram and opposite sides of a parallelogram are parallel,

  $GR\parallel MA$

Take GM as a transversal

  $\angle G+\angle M=180°$

(If a transversal intersects two parallel lines then each pair of interior angles on the same side of transversal are supplementary that is sum of interior angles is equal to $180°$ )

b.

To determine

To state: the reason why $\angle M$ is supplementary to $\angle A$

Explanation of Solution

  

As $GRAM$ is a parallelogram and opposite sides of a parallelogram are parallel,

  $GR\parallel MA$

Take GM as a transversal

  $\angle M+\angle A=180°$

(If a transversal intersects two parallel lines then each pair of interior angles on the same side of transversal are supplementary, that is sum of interior angles is equal to $180°$ )

c.

To determine

To complete: the given statement

Explanation of Solution

  

Consecutive angles of a parallelogram are supplementary while opposite angles are equal.