Question

write a two - column proof. given m∠gfi = 141°. prove m∠efi = 45°. 1 m∠gfi = 141° 1 given 2 m∠gfe + m∠efi = m∠gfi 2 angle addition postulate 3 m∠gfe + m∠efi = 141° 3 substitution property, (steps 1, 2) 4 m∠gfe=(8x - 3)°, m∠efi = 4x° 4 given 5 8x - 3+4x = 141 5 substitution property 6 12x - 3 = 141 5 combine like terms. 7 12x = 144 7 addition property of equality 8 x = 8 division property of equality

Explanation:

Step1: Combine like - terms in equation

We have the equation $8x - 3+4x = 141$. Combining the $x$ - terms, $8x+4x=12x$, so the equation becomes $12x - 3=141$.

Step2: Isolate the term with $x$

Add 3 to both sides of the equation $12x - 3=141$. Using the addition property of equality, $12x-3 + 3=141 + 3$, which simplifies to $12x=144$.

Step3: Solve for $x$

Divide both sides of the equation $12x = 144$ by 12. Using the division property of equality, $\frac{12x}{12}=\frac{144}{12}$, so $x = 12$.

Answer:

$x = 12$