Question

write a two - column proof. given: m∠gfi = 141°. prove: m∠efi = 48°. statements: 1. m∠gfi = 141°. reason: 1. given. 2. m∠gfe + m∠efi=m∠gfi. reason: 2.

Explanation:

Step1: Recall angle - addition postulate

The angle - addition postulate states that if point $E$ lies in the interior of $\angle GFI$, then $m\angle GFE+m\angle EFI = m\angle GFI$.

Step2: Substitute given values

We know that $m\angle GFI = 141^{\circ}$ and $m\angle GFE=93^{\circ}$. Let $m\angle EFI=x$. Then, from the angle - addition postulate $93^{\circ}+x = 141^{\circ}$.

Step3: Solve for $x$

Subtract $93^{\circ}$ from both sides of the equation: $x=m\angle EFI=141^{\circ}-93^{\circ}=48^{\circ}$.

Answer:

$m\angle EFI = 48^{\circ}$