Question

1. m∠e = m∠g =

Explanation:

Step1: Recall triangle - angle - sum property

The sum of the interior angles of a triangle is 180°. In \(\triangle EFG\), we know that \(\angle F = 106^{\circ}\), and since \(EF = FG\) (the equal - side markings), \(\angle E=\angle G\). Let \(m\angle E = m\angle G=x\).

Step2: Set up an equation

Using the angle - sum property of a triangle, we have \(x + x+106^{\circ}=180^{\circ}\), which simplifies to \(2x+106^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, subtract \(106^{\circ}\) from both sides of the equation: \(2x=180^{\circ}- 106^{\circ}=74^{\circ}\). Then divide both sides by 2: \(x = 37^{\circ}\).

Answer:

\(m\angle E = 37^{\circ}\), \(m\angle G = 37^{\circ}\)