Question

write a two - column proof. given: m∠gfi = 127°. prove: m∠efi = 40°. statements: 1. m∠gfi = 127°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 127°. 4. m∠gfe=(9x - 3)°, m∠efi = 4x°. 5. 9x - 3+4x = 127. 6. blank=127. 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 9x - 3+4x

Combining 9x and 4x gives 13x. So, 9x - 3+4x = 13x - 3.

Step2: Solve for x

We have the equation 13x - 3 = 127. Add 3 to both sides: 13x-3 + 3=127 + 3, which simplifies to 13x = 130. Then divide both sides by 13: $x=\frac{130}{13}=10$.

Step3: Find m∠EFI

Since m∠EFI = 4x°, substitute x = 10 into the expression. So, m∠EFI = 4×10° = 40°.

Answer:

m∠EFI = 40°