Chapter 9.5, Problem 22WE

To determine

To find: The value of angle A .

Answer to Problem 22WE

The value of A is $90°$ .

Explanation of Solution

Given:

ABCD is parallelogram inscribed in circle.

Calculation:

Sum of angle B and C is 180 degree as one-sided interior angle.

  $\begin{array}{l}\angle B+\angle C=180°\\ \angle C=180°-\angle B\mathrm{......}\left(1\right)\end{array}$

And,

  $\angle B+\angle A=180°\mathrm{......}\left(2\right)$

Opposite angle of cyclic quadrilateral is supplementary.

Thus,

  $\angle C+\angle A=180°$

Substitute the values of C from equation (1) as follows:

  $\begin{array}{l}180°-\angle B+\angle A=180°\\ \angle A=\angle B\end{array}$

Substitute angle A for B in equation (2) as follows:

  $\begin{array}{c}\angle A+\angle A=180°\\ 2\angle A=180°\\ \angle A=90°\end{array}$

Thus, the value of A is $90°$ .