Question

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

m∠efa=

#7 #8 #9 #10 #24 #40 #54 #69 #111 #126 #140 #156

Explanation:

Step1: Use angle - addition property

Since $\angle AFC = 90^{\circ}$ and $\angle AFC=\angle AFB+\angle BFC$, we have $(3x + 27)+4x=90$.

Step2: Combine like - terms

Combining the $x$ terms, we get $3x+4x+27 = 90$, which simplifies to $7x+27 = 90$.

Step3: Solve for $x$

Subtract 27 from both sides: $7x=90 - 27=63$. Then divide both sides by 7, so $x = 9$.

Step4: Find $\angle AFB$

Substitute $x = 9$ into the expression for $\angle AFB$: $\angle AFB=3x + 27=3\times9+27=27 + 27=54^{\circ}$.

Step5: Use vertical - angle property

$\angle EFD=\angle AFC = 90^{\circ}$ (vertical angles).
$\angle EFA=\angle BFC$ (vertical angles). Substitute $x = 9$ into the expression for $\angle BFC$, $\angle BFC = 4x=4\times9 = 36^{\circ}$, so $\angle EFA = 36^{\circ}$.

Answer:

$m\angle EFD = 90$
$m\angle EFA = 36$