Chapter E, Problem 4.11EX

To determine

To Find:

The measure of $\angle CBD$ .

Answer to Problem 4.11EX

The measure of $\angle CBD$ is option (b) $44$ .

Explanation of Solution

Given information:

In triangle $△ABC$ , $AB=AC,m\angle A=46$ and $B\overline{D}$ is an altitude.

Consider the $△ABC$ where $AB=AC$ .

If the opposite sides are equal then opposite angles are equal. Hence, if $m\angle A=46$ then $m\angle C=46$

Sum of interior angles is ${180}^{\circ }$ .

  $\begin{array}{l}m\angle A+m\angle B+m\angle C=180\\ 46+m\angle B+46=180\\ 92+m\angle B=180\\ m\angle B=180-92=88\end{array}$

Since BD is an altitude, $\angle CBD=44$

Therefore, the measure of $\angle CBD$ is option (b) $44$ .