Chapter 5.5, Problem 10WE

To determine

To find: The values of other angles of isosceles trapezoid.

Answer to Problem 10WE

The values of angles A , B , C and D are 57, 123, 123 and 57 respectively.

Explanation of Solution

Given:

Consider the trapezoid as shown below:

  

The angle A is 57.

Calculation:

For the isosceles trapezoid,

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

Hence,

  $\angle A=\angle D=57$

Sum of one sided interior angles must be 180.

Hence,

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

And,

  $\angle B=\angle C=123$

Thus, the values of angles A , B , C and D are 57, 123, 123 and 57 respectively.