Question

angle cad is bisected by ray ab. the measure of angle cab = 4x + 1. the measure of angle cad is 66. find the value of x.

Explanation:

Step1: Recall angle - bisector property

Since ray AB bisects angle CAD, then $\angle CAD = 2\angle CAB$.

Step2: Substitute given values

We know that $\angle CAD = 66$ and $\angle CAB=4x + 1$. So, $66=2(4x + 1)$.

Step3: Solve the equation

First, distribute the 2 on the right - hand side: $66 = 8x+2$. Then subtract 2 from both sides: $66 - 2=8x$, which gives $64 = 8x$. Finally, divide both sides by 8: $x=\frac{64}{8}=8$.

Answer:

$8$