Question

in the figure, ba and bc are opposite rays. bh bisects ∠ebc and be bisects ∠abf. if m∠ebh=(6x + 12)° and m∠hbc=(8x - 10)°, find m∠ebh.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BH}$ bisects $\angle EBC$, we know that $m\angle EBH=m\angle HBC$. So, $6x + 12=8x-10$.

Step2: Solve the equation for $x$

Subtract $6x$ from both sides: $12 = 8x-6x - 10$, which simplifies to $12=2x - 10$. Then add 10 to both sides: $12 + 10=2x$, so $22 = 2x$. Divide both sides by 2: $x = 11$.

Step3: Find $m\angle EBH$

Substitute $x = 11$ into the expression for $m\angle EBH$. $m\angle EBH=6x + 12$. So, $m\angle EBH=6\times11+12=66 + 12=78$.

Answer:

78