Question

question
in △efg, ef ≅ ge and m∠e = 141°, find m∠g.
answer

Explanation:

Step1: Identify the triangle type

Since \(EF\cong GE\), \(\triangle EFG\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. But \(\angle E = 141^{\circ}\) is the vertex angle.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle F=\angle G = x\). Then \(x + x+141^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 141^{\circ}\).
\(2x = 39^{\circ}\).
Solve for \(x\): \(x=\frac{39^{\circ}}{2}=19.5^{\circ}\).

Answer:

\(19.5^{\circ}\)