Question

Given that $m\angle \text{CAB}={33}^{\circ }$ and AB bisects $\angle \text{CAD}$ into two equal halves $\angle \text{CAB}$ and $\angle \text{DAB}$ respectively. What is the value of $x$?

• A.
  $4$
• B.
  $8$
• C.
  $6$
• D.
  $10$

Answer 1

The correct option is B

$8$

Given that,

$m\angle \text{CAD}={33}^{\circ }$

$m\angle \text{CAD}=(4x+1{)}^{\circ }$

AB is an angle bisector. So,
$\angle \text{DAB}=\angle \text{CAB}$

$(4x+1{)}^{\circ }={33}^{\circ }$

$4x=(33-1{)}^{\circ }$

$4x={32}^{\circ }$

$x=\frac{{32}^{\circ }}{4}$

$x=8$