Question

write a two - column proof.
given: m∠gfi = 127°
prove: m∠efi = 33°

1. m∠gfe + m∠efi = m∠gfi 2. angle addition postulate
2. m∠gfe + m∠efi = 127° 3. substitution property, (steps 1, 2)
3. m∠gfe=(9x - 5)°, m∠efi = 3x° 4. given
4. 9x - 5+3x = 127 5. substitution property
5. 12x - 5 = 127 6. combine like terms
6. 12x = 132 7. addition property of equality
7. x = 8. division property of equality

Explanation:

Step1: Isolate the variable term

Starting from $12x - 5=127$, we want to get $12x$ alone. By the addition property of equality, we add 5 to both sides of the equation. So, $12x-5 + 5=127 + 5$, which simplifies to $12x=132$.

Step2: Solve for x

We have the equation $12x = 132$. By the division property of equality, we divide both sides of the equation by 12. So, $x=\frac{132}{12}$.

Answer:

$x = 11$