Question

m<afb=(3x + 27)° and m<bfc=(4x)°. find m∠efd = m∠efa =

Explanation:

Step1: Note that ∠AFB and ∠BFC are complementary

Since ∠AFC = 90°, we have m∠AFB + m∠BFC=90°. So, (3x + 27)+4x=90.

Step2: Solve the equation for x

Combining like - terms, we get 7x+27 = 90. Subtract 27 from both sides: 7x=90 - 27=63. Then divide both sides by 7: x = 9.

Step3: Find m∠AFB

Substitute x = 9 into the expression for m∠AFB: m∠AFB=3x + 27=3×9+27=27 + 27=54°.

Step4: Use vertical - angle property

∠EFD and ∠AFC are vertical angles. Since ∠AFC = 90°, m∠EFD = 90°.

Step5: Use the fact that ∠EFA and ∠AFB are vertical angles

Since vertical angles are congruent, m∠EFA=m∠AFB. So m∠EFA = 54°.

Answer:

m∠EFD = 90°
m∠EFA = 54°