Question

write a two - column proof. given: m∠gfi = 127°. prove: m∠efi = 33°. 1. m∠gfi = 127° 1. given 2. m∠gfe + m∠efi = m∠gfi 2. angle addition postulate 3. m∠gfe + m∠efi = 127° 3. substitution property. (steps 1, 2) 4. m∠gfe=(9x - 5)°, m∠efi = 3x° 4. given 5. 9x - 5+3x = 127 5. substitution property 6. 12x - 5 = 127 6. combine like terms. 7. x = 7. addition property of equality

Explanation:

Step1: Add 5 to both sides

$12x-5 + 5=127 + 5$

Step2: Simplify both sides

$12x=132$

Step3: Divide both sides by 12

$x=\frac{132}{12}$

Step4: Calculate the value of x

$x = 11$

Step5: Find the measure of $\angle EFI$

Since $m\angle EFI=3x^{\circ}$, substitute $x = 11$. So $m\angle EFI=3\times11^{\circ}=33^{\circ}$

Answer:

$x = 11$ and $m\angle EFI=33^{\circ}$