Question

7.
8.
$m\angle e=$
$x=$
$m\angle g=$

Explanation:

Step1: Solve for \(x\) in the equilateral triangle (Problem 7)

An equilateral triangle has all angles equal to \(60^{\circ}\). So, \(9x - 3=60\).
Add \(3\) to both sides: \(9x=60 + 3=63\).
Divide both sides by \(9\): \(x=\frac{63}{9}=7\).

Step2: Find angles in the isosceles triangle \(EFG\) (Problem 8)

In \(\triangle EFG\), \(EF = FG\), so \(\angle E=\angle G\).
The sum of angles in a triangle is \(180^{\circ}\). Let \(m\angle E = m\angle G=y\).
We know \(y + y+104^{\circ}=180^{\circ}\).
Combine like - terms: \(2y=180^{\circ}- 104^{\circ}=76^{\circ}\).
Divide both sides by \(2\): \(y = 38^{\circ}\).

Answer:

1. \(x = 7\)
2. \(m\angle E=38^{\circ}\), \(m\angle G = 38^{\circ}\)