Find the measure of angle EBH:
In the figure, $\overrightarrow{B A}$ and $\overrightarrow{B C}$ are opposite rays. $\overrightarrow{B H}$ bisects $\angle E B C$ and $\overrightarrow{B E}$ bisec $^{+} \angle A B F$.
If $m \angle E B H=(6 x+12)^{\circ}$ and $m \angle H B C=(8 x-10)^{\circ}$, find $m \angle E B H$.
Answer
Therefore, the measure of angle EBH is \(\boxed{78}\) degrees.
Step 1 ：Given that line BH bisects angle EBC, we know that angle EBH equals angle HBC. Therefore, we can set up the equation \((6x+12)^{\circ} = (8x-10)^{\circ}\) and solve for x.
Step 2 ：Solving the equation, we find that x equals 11.
Step 3 ：Substituting x = 11 back into the expression for m angle EBH, we find that m angle EBH equals 78 degrees.
Step 4 ：Therefore, the measure of angle EBH is \(\boxed{78}\) degrees.
