Question

write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. statements: 1. m∠gfi = 131°. reasons: 1. given. 2. m∠gfe + m∠efi = m∠gfi. 2. angle addition postulate. 3. m∠gfe + m∠efi = blank°. 3. substitution property, (steps 1, 2)

Explanation:

Step1: Identify given angle

We know $\angle GFI = 131^{\circ}$ from the given information.

Step2: Apply angle - addition postulate

By the Angle Addition Postulate, $\angle GFE+\angle EFI=\angle GFI$.

Step3: Substitute the value of $\angle GFI$

Since $\angle GFI = 131^{\circ}$, we substitute it into the equation $\angle GFE+\angle EFI=\angle GFI$ to get $\angle GFE+\angle EFI = 131^{\circ}$. Also, we know that $\angle GFE=(8x - 1)^{\circ}$ and $\angle EFI = 3x^{\circ}$, so $(8x-1)+3x=131$.
Combining like - terms:
$8x+3x-1 = 131$
$11x-1=131$
Adding 1 to both sides:
$11x=131 + 1$
$11x=132$
Dividing both sides by 11:
$x = 12$
Then $\angle EFI=3x^{\circ}$, substituting $x = 12$ gives $\angle EFI=3\times12^{\circ}=36^{\circ}$.

Answer:

$131$