Question

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

Explanation:

Step1: Use the angle - bisector property

Since \(HF\) is the angle bisector of \(\angle EHG\), then \(m\angle EHF=m\angle FHG\). Given \(m\angle EHG = 68^{\circ}\), and \(m\angle FHG=9x - 2\). By the angle - bisector definition, \(m\angle EHF=m\angle FHG\), and \(m\angle EHG=m\angle EHF + m\angle FHG\). So \(m\angle EHG = 2m\angle FHG\) (because \(m\angle EHF=m\angle FHG\)).

Step2: Substitute the values into the equation

Substitute \(m\angle EHG = 68^{\circ}\) and \(m\angle FHG=9x - 2\) into \(m\angle EHG = 2m\angle FHG\). We get the equation \(68=2(9x - 2)\).

First, expand the right - hand side of the equation: \(68 = 18x-4\).

Then, add \(4\) to both sides of the equation: \(68 + 4=18x-4 + 4\), which simplifies to \(72=18x\).

Finally, divide both sides by \(18\): \(x=\frac{72}{18}\).

Answer:

\(x = 4\)