Question

write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. statements: 1. m∠gfi = 131°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 131°. 4. m∠gfe=(8x - 1)°, m∠efi = 3x°. 5. 8x - 1+3x = 131. 6. = 131. reasons: 1. given. 2. angle addition postulate. 3. substitution property, (steps 1, 2). 4. given. 5. substitution property. 6. combine like terms.

Explanation:

Step1: Combine like - terms in the equation

Combining $8x-1 + 3x=131$, we get $(8x + 3x)-1=131$, which simplifies to $11x-1 = 131$.

Step2: Solve for $x$

Add 1 to both sides of the equation $11x-1 = 131$. We have $11x-1+1=131 + 1$, so $11x=132$. Then divide both sides by 11: $\frac{11x}{11}=\frac{132}{11}$, and $x = 12$.

Step3: Find the measure of $\angle EFI$

Since $m\angle EFI=3x^{\circ}$ and $x = 12$, then $m\angle EFI=3\times12^{\circ}=36^{\circ}$.

Answer:

$11x - 1$ (for the blank in the two - column proof) and $m\angle EFI = 36^{\circ}$