Question

1. ray hf is an angle bisector of ∠ehg. m∠ehg = 68° and m∠fhg = 9x - 2. find the value of x.

m∠ehf + m∠fhg = m∠ehg

Explanation:

Step1: Use angle - bisector property

Since $HF$ is the angle - bisector of $\angle EHG$, then $m\angle EHF=m\angle FHG$. And we know that $m\angle EHF + m\angle FHG=m\angle EHG$, so $2m\angle FHG=m\angle EHG$.

Step2: Substitute the given values

We are given that $m\angle EHG = 68^{\circ}$ and $m\angle FHG=9x - 2$. Substituting into $2m\angle FHG=m\angle EHG$, we get $2(9x - 2)=68$.

Step3: Expand the left - hand side

Using the distributive property $a(b - c)=ab-ac$, we have $18x-4 = 68$.

Step4: Add 4 to both sides

$18x-4 + 4=68 + 4$, which simplifies to $18x=72$.

Step5: Solve for x

Dividing both sides by 18, we get $x=\frac{72}{18}=4$.

Answer:

$x = 4$