Question

write a two - column proof. given: m∠gfi = 152°. prove: m∠efi = 48°. statements: 1. m∠gfi = 152°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 152°. 4. m∠gfe=(9x - 4)°, m∠efi = 4x°. 5. 9x - 4+4x = 152. 6. □ = 152. 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

Combine $9x - 4+4x$ to get $13x - 4$. So the equation in step 5 becomes $13x-4 = 152$.

Step2: Solve for $x$

Add 4 to both sides of the equation $13x-4 = 152$. We get $13x=152 + 4$, so $13x=156$. Then divide both sides by 13, $x=\frac{156}{13}=12$.

Step3: Find the measure of $\angle EFI$

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

Answer:

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