Question

10.
e

f
106°

g

m∠e = ______
m∠g = ______

Explanation:

Step1: Identify Triangle Type

The triangle \( \triangle EFG \) has \( EF = FG \) (marked with ticks), so it's isosceles with \( \angle E \cong \angle G \).

Step2: Sum of Angles in Triangle

The sum of angles in a triangle is \( 180^\circ \). Let \( m\angle E = m\angle G = x \). Then:
\( x + x + 106^\circ = 180^\circ \)

Step3: Solve for \( x \)

Simplify: \( 2x = 180^\circ - 106^\circ = 74^\circ \)
Divide: \( x = \frac{74^\circ}{2} = 37^\circ \)

Answer:

\( m\angle E = 37^\circ \)
\( m\angle G = 37^\circ \)