Question

write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 33°. statements: 1. m∠gfi = 131°. 2. m∠gfe + m∠efi = m∠gfi. 3. m∠gfe + m∠efi = 131°. 4. m∠gfe=(9x - 1)°, m∠efi = 3x°. 5. 9x - 1+3x = 131. 6. = 131. 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 equation

Combine $9x$ and $3x$ in the equation $9x - 1+3x = 131$.
$12x-1 = 131$

Step2: Add 1 to both sides

To isolate the term with $x$, add 1 to both sides of the equation.
$12x-1 + 1=131 + 1$
$12x=132$

Step3: Solve for x

Divide both sides of the equation by 12.
$x=\frac{132}{12}=11$

Step4: Find m∠EFI

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

Answer:

$33^{\circ}$