Chapter E, Problem 3.11EX

To determine

To find the measure of the $\angle ACD$ .

Answer to Problem 3.11EX

Option (c) $72$ is correct.

Explanation of Solution

Given information: $\overline{AC}$ is a diagonal of regular pentagon ABCDE.

Options,

a. $36$

b. $54$

c. $72$

d. $108$

Calculation: The required solutions is obtained as,

Let the sides be x

Each interior angle $=180$ degree (Regular polygon).

In $\Delta ABC$

  $AB=BC$

Hence $\angle BAC=\angle BCA=m$ ( Isosceles triangle)

  $\begin{array}{l}\left(\angle m+\angle m+△ABC\right)=180\\ 2\left(\angle m\right)=180-108\\ \angle m=36\\ \angle ACD=\angle BCD-\angle m=108-36=72\end{array}$

Therefore, option (c) $72$ is correct.