Chapter 7.1, Problem 16PSB

To determine

To calculate : The value of $m\angle D$ .

Answer to Problem 16PSB

The value of $m\angle D$ is ${117.5}^0$

Explanation of Solution

Given information : The following information is given

  $\angle A={30}^0$

  $\overrightarrow{AB}\cong \overrightarrow{AC}$

CD bisects $\angle ACB$

BD is one of the trisectors of $\angle ABC$

Formula used : The angles of any triangle add up to ${180}^0$

Calculation : We know that $\overrightarrow{AB}\cong \overrightarrow{AC}$ , hence we can say that

  $\angle B\cong \angle C$

Thus, we know that the angles of any triangle add up to ${180}^0$ . Thus, we add up the angles

  ${30}^0+2\angle B={180}^0\to \angle B={75}^0=\angle C$

Now, we know that

  $\angle DBC=\frac{1}{3}\angle B={25}^0$

Also, $\angle DCB=\frac{1}{2}\angle C={37.5}^0$

Now, in triangle DBC, we have

  $\angle D+{37.5}^0+{25}^0={180}^0$

Hence, the value of $m\angle D$ is ${117.5}^0$