Question

write a two - column proof. given: m∠gfi = 127°. prove: m∠efi = 44°. statements: 1. m∠gfi = 127°. reasons: 1. given. 2. m∠gfe + m∠efi = m∠gfi. 2. angle addition postulate. 3. m∠gfe + m∠efi = 127°. 3. substitution property, (steps 1, 2)

Explanation:

Step1: Apply substitution

Since \(m\angle GFI = 127^{\circ}\) and \(m\angle GFE + m\angle EFI=m\angle GFI\), substituting \(m\angle GFI\) gives \(m\angle GFE + m\angle EFI = 127^{\circ}\).

Step2: Set up an equation using angle - measures

We know that \(m\angle GFE=(8x - 5)^{\circ}\) and \(m\angle EFI = 4x^{\circ}\). So \((8x - 5)+4x=127\).

Step3: Combine like - terms

\(8x+4x-5 = 127\), which simplifies to \(12x-5 = 127\).

Step4: Solve for \(x\)

Add 5 to both sides: \(12x=127 + 5=132\). Then divide both sides by 12, so \(x = 11\).

Step5: Find \(m\angle EFI\)

Since \(m\angle EFI = 4x^{\circ}\), substituting \(x = 11\) gives \(m\angle EFI=4\times11^{\circ}=44^{\circ}\).

Answer:

127