Question

One angle of an isosceles trapezoid has measured 57. Find the measures of the other angles.

Short answer

The measure of other angles is $\mathbf{57}\mathbf{,}\mathbf{}\mathbf{123}$and 123.

Step-by-step solution

Step 1. Draw and label the diagram.

The figure shows, isosceles trapezoid. Let the measure of angle B be 57.

Step 2. Apply the property of isosceles trapezoid.

The base angles of an isosceles trapezoid are congruent.

Consider an isosceles trapezoid ABCD such that,

$\begin{array}{l}\angle A\cong \angle D;\\ \angle B\cong \angle C\end{array}$

Therefore$m\angle B=m\angle C=57$

Step 3. Description of step.

The sum of the same side interior angles is 180. Therefore,

$\begin{array}{c}m\angle A+m\angle B=180\\ m\angle A+57=180\\ m\angle A=180-57\\ =123\end{array}$

Step 4. Description of step.

Substitute 123 for $m\angle A$into $m\angle A=m\angle D$to find the value of $m\angle D$.

$m\angle D=123$

Therefore, the measure of other angles is $57,123$and $123$.