Chapter 9, Problem 14CT

To determine

To find: the value of angle AEC .

Answer to Problem 14CT

The angle $m\angle AEC$ is 34.

Explanation of Solution

Given:

The circle is shown below:

Arcs AC and BD are 40 and 28 respectively.

Calculation:

For circle with intersecting cord as shown below:

The angle formed by the intersecting cord is,

  $\angle 1=\frac{1}{2}\left(arcAB+arcDC\right)$

For given circle,

The angle $m\angle AEC$ is calculated as follows:

  $\begin{array}{c}m\angle AEC=\frac{1}{2}\left(arcAC+arcBD\right)\\ =\frac{1}{2}\left(40+28\right)\\ =34\end{array}$

Hence, the angle $m\angle AEC$ is 34.