Question

bonus question
lines ab and bc intersect at point b. ray bd bisects angle abc.
find the measure of <abd.
(x + 8)°
(4x - 30)°

Explanation:

Step1: Set up equation

Since ray $BD$ bisects $\angle ABC$, we have $\angle ABD=\angle DBC$. So $x + 8=4x-30$.

Step2: Solve for $x$

Subtract $x$ from both sides: $8 = 3x-30$. Then add 30 to both sides: $38=3x$. So $x=\frac{38}{3}$.

Step3: Find $\angle ABD$

Substitute $x = \frac{38}{3}$ into the expression for $\angle ABD$ which is $x + 8$. So $\angle ABD=\frac{38}{3}+8=\frac{38 + 24}{3}=\frac{62}{3}=20\frac{2}{3}$ degrees.

Answer:

$20\frac{2}{3}$ degrees