Question

in the diagram to the right, ∠afe is a straight angle and ∠cfe is a right angle. identify all supplementary and complementary angles. then, find m∠dfe, m∠bfc, and m∠bfe.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90°, and supplementary angles add up to 180°.

Step2: Identify complementary angles

Since ∠CFE = 90°, ∠BFC and ∠BFE are complementary (because ∠BFC+∠BFE = ∠CFE = 90°). Also, ∠DFE and ∠CFD are complementary as ∠CFD = 42° and ∠DFE+42°=90°.

Step3: Identify supplementary angles

Since ∠AFE = 180°, ∠AFB and ∠BFE are supplementary (because ∠AFB + ∠BFE=∠AFE = 180°).

Step4: Find m∠DFE

We know that ∠CFE = 90° and ∠CFD = 42°. So, m∠DFE=90° - 42° = 48°.

Step5: Find m∠BFC

We know that ∠AFE = 180°, ∠AFB = 39°, and ∠CFE = 90°. First, find ∠BFE=180° - 39°=141°. Since ∠CFE = 90°, m∠BFC=90° - 39° = 51°.

Step6: Find m∠BFE

m∠BFE=180° - 39° = 141°.

Answer:

Complementary angles: ∠BFC and ∠BFE, ∠DFE and ∠CFD.
Supplementary angles: ∠AFB and ∠BFE.
m∠DFE = 48°, m∠BFC = 51°, m∠BFE = 141°