Question

write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. statements: 1. m∠gfi = 131°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 131°. 4. m∠gfe=(8x - 1)°, m∠efi = 3x°. 5. 8x - 1+3x = 131. 6. 11x - 1 = 131. 7. 11x = 132. 8. x = . reasons: 1. given. 2. angle addition postulate. 3. substitution property, (steps 1, 2). 4. given. 5. substitution property. 6. combine like terms. 7. addition property of equality. 8. division property of equality.

Explanation:

Step1: Combine like - terms in equation

Starting from $11x - 1=131$, we want to isolate the term with $x$.

Step2: Apply addition property of equality

Add 1 to both sides of the equation $11x - 1=131$. So, $11x-1 + 1=131 + 1$, which simplifies to $11x=132$.

Step3: Apply division property of equality

Divide both sides of the equation $11x = 132$ by 11. So, $\frac{11x}{11}=\frac{132}{11}$, and we get $x = 12$.

Answer:

$12$