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11 votes
11 votes
m∠AFD=90°. m∠AFB=31°. Find m∠DFE.Point C is in the interior of angle AFE. Point B is in the interior of angle AFC. Point D is in the interior of angle CFE. Angle AFB is congruent to angle CFD. Angle cFB is congruent to angle DFE.A. 28B. 29.5C. 31D. 87

m∠AFD=90°. m∠AFB=31°. Find m∠DFE.Point C is in the interior of angle AFE. Point B-example-1
User Rodvlopes
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1 Answer

10 votes
10 votes

ANSWER:

A. 28

Explanation:

Given:

m∠AFD = 90°

m∠AFB = 31°

From the graph, we can establish that ∠AFD is equal to the sum of angles ∠AFB, ∠CFB, and ∠CFD.

We can pose the following equation, knowing also that ∠AFB and ∠CFD are equal:


\begin{gathered} \angle AFD=\angle AFB+\angle CFB+\angle CFD \\ \\ \angle AFB=\angle CFD,\text{ therefore:} \\ \\ \angle AFD=\angle AFB+\angle CFB+\angle AFB \\ \\ \angle AFD=2\cdot\angle AFB+\angle CFB \\ \\ \text{ We replacing:} \\ \\ 90\degree=2\cdot31\degree+\angle CFB \\ \\ \angle CFB=90\degree-2\cdot31\degree=90\degree-62\degree \\ \\ \angle CFB=28\degree \\ \\ \text{ and we know that the angle \angle CFB is equal to \angle DFE:} \\ \\ ∠DFE=\operatorname{\angle}CFB=28\operatorname{\degree} \end{gathered}

Therefore, the correct answer is A. 28

User David Hyde
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