Textbook Problem

Consider $▱$ ABCD as shown.

a) How are $\angle A$ and $\angle C$ related?

b) How are $\angle A$ and $\angle B$ related?

To determine

To Find:

The relation between $\angle A$ and $\angle C$.

Answer to Problem 1CT

Solution:

$\angle A$ and $\angle C$ are congruent angles.

Explanation of Solution

Given parallelogram,

From the property opposite angles in a parallelogram are congruent.

Since ABCD is a parallelogram, $\angle A$ and $\angle C$ are opposite angles then $\angle A$ and $\angle C$ are congruent angles.

The Final statement:

$\angle A$ and $\angle C$ are congruent angles.

To determine

To Find:

The relation between $\angle A$ and $\angle B$.

Answer to Problem 1CT

Solution:

$\angle A$ and $\angle B$ are supplementary angles.

Explanation of Solution

Given parallelogram,

From the property consecutive angles in a parallelogram are supplementary.

Since ABCD is a parallelogram, $\angle A$ and $\angle B$ are consecutive angles then $\angle A$ and $\angle B$ are supplementary angles.

The Final statement:

$\angle A$ and $\angle B$ are supplementary angles.