Question

write a two - column proof. given: m∠gfi = 141°. prove: m∠efi = 48°. statements: 1. m∠gfi = 141°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 141°. 4. m∠gfe=(8x - 3)°, m∠efi = 4x°. 5. 8x - 3+4x = 141. 6. = 141. 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

Combine the $x$ terms in the equation $8x - 3+4x = 141$. We add the coefficients of $x$: $(8 + 4)x-3=141$, so $12x-3 = 141$.

Step2: Solve for $x$

Add 3 to both sides of the equation $12x-3 = 141$. We get $12x-3 + 3=141 + 3$, which simplifies to $12x=144$. Then divide both sides by 12: $x=\frac{144}{12}=12$.

Step3: Find $m\angle EFI$

Since $m\angle EFI = 4x^{\circ}$ and $x = 12$, then $m\angle EFI=4\times12^{\circ}=48^{\circ}$.

Answer:

$12x - 3$ (for the blank in step 6 of the given proof); $m\angle EFI = 48^{\circ}$ is proven as shown above.