Question

in the diagram below, $overline{ad}$ bisects $angle cab$, $mangle adb = 99^{circ}$ and $mangle cad = 31^{circ}$. find $mangle b$. you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale. answer attempt 1 out of 2 $mangle b=square^{circ}$

Explanation:

Step1: Find measure of ∠CAB

Since $\overline{AD}$ bisects $\angle CAB$ and $m\angle CAD = 31^{\circ}$, then $m\angle CAB=2\times m\angle CAD$.
$m\angle CAB = 2\times31^{\circ}=62^{\circ}$

Step2: Find measure of ∠B in △ABD

In $\triangle ABD$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. We know $m\angle ADB = 99^{\circ}$ and $m\angle BAD=m\angle CAD = 31^{\circ}$. Let $m\angle B=x$. Then $x + 99^{\circ}+31^{\circ}=180^{\circ}$.
$x=180^{\circ}-(99^{\circ} + 31^{\circ})$
$x = 180^{\circ}-130^{\circ}$
$x = 50^{\circ}$

Answer:

$50$