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 = °. reasons: 1. given; 2. angle addition postulate; 3. substitution property, (steps 1, 2)

Explanation:

Step1: Identify given angle

Given \(m\angle GFI = 131^{\circ}\)

Step2: Apply angle - addition postulate

By the Angle Addition Postulate, \(m\angle GFE+m\angle EFI=m\angle GFI\)

Step3: Substitute the value of \(m\angle GFI\)

Since \(m\angle GFI = 131^{\circ}\), then \(m\angle GFE + m\angle EFI=131^{\circ}\) (by Substitution Property)
We also know that \(m\angle GFE=(9x - 1)^{\circ}\) and \(m\angle EFI = 3x^{\circ}\), so \((9x-1)+3x=131\).
Combining like - terms: \(9x+3x-1 = 131\), \(12x-1=131\).
Adding 1 to both sides: \(12x=132\).
Dividing both sides by 12: \(x = 11\).
Then \(m\angle EFI=3x^{\circ}=3\times11^{\circ}=33^{\circ}\)

Answer:

131