Question

1. if bd bisects ∠abc, m∠dbc = 84, and m∠abc=(9x - 3), find the value of x.

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABC = 2m\angle DBC$.

Step2: Substitute given values

We know $m\angle DBC = 84$ and $m\angle ABC=(9x - 3)$. So, $9x-3=2\times84$.

Step3: Simplify the right - hand side

$9x - 3=168$.

Step4: Solve for x

Add 3 to both sides: $9x=168 + 3$, so $9x=171$. Then divide both sides by 9: $x=\frac{171}{9}=19$.

Answer:

$x = 19$