Chapter 9.2, Problem 7PSA

a

To determine

To find:The value of $m\angle A$

Answer to Problem 7PSA

The value of $m\angle A={40}^0$

Explanation of Solution

Given information:The following information has been given

Measure of arc BC is ${80}^0$

Formula used:The angle subtended by the arc at the center is double the measure of the angle subtended at any point on the circumference of the circle.

Calculation:We know that the angle subtended by the arc at the center is double the measure of the angle subtended at any point on the circumference of the circle. Hence, we can say that

  $m\angle A=\frac{1}{2}({80}^0)={40}^0$

b

To determine

To find:The value of $m\angle D$

Answer to Problem 7PSA

The value of $m\angle D={40}^0$

Explanation of Solution

Given information:The following information has been given

Measure of arc BC is ${80}^0$

Formula used:The angle subtended by the arc at the center is double the measure of the angle subtended at any point on the circumference of the circle.

Calculation:We know that the angle subtended by the arc at the center is double the measure of the angle subtended at any point on the circumference of the circle.

Now, we apply the same formula here of arc BC. Hence, we can say that

  $m\angle D=\frac{1}{2}({80}^0)={40}^0$