Question

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

Explanation:

Step1: Identify isosceles - triangle

Since $EF\cong GF$ in $\triangle EFG$, $\triangle EFG$ is an isosceles triangle with base - angles $\angle E$ and $\angle G$ equal.

Step2: Use angle - sum property

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle E = m\angle G=x$. We know $m\angle F = 141^{\circ}$. So, $x + x+141^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Combining like - terms gives $2x=180^{\circ}-141^{\circ}=39^{\circ}$. Then $x = \frac{39^{\circ}}{2}=19.5^{\circ}$.

Answer:

$19.5^{\circ}$