Question

4 using the diagram below, identify a set of complementary and a set of supplementary angles. then find m∠dfe, m∠bfc, and m∠bfe
set of complementary angles:
∠dfe
∠bfc = 39 m = bfe 124
set of supplementary angles:
∠afb
∠bfe
m∠dfe = 90 - 27 = 63
m∠bfc = 180 - 39 = 141
m∠bfe = 180 - 79 = 101

Explanation:

Step1: Recall angle - sum properties

Complementary angles sum to $90^{\circ}$, supplementary angles sum to $180^{\circ}$.

Step2: Find $m\angle DFE$

Since $\angle BFA = 39^{\circ}$ and $\angle BFA+\angle DFE = 90^{\circ}$ (complementary), then $m\angle DFE=90 - 39=53^{\circ}$.

Step3: Find $m\angle BFC$

Given $\angle CFD = 27^{\circ}$ and $\angle BFC+\angle CFD = 90^{\circ}$ (assuming $\angle BFD = 90^{\circ}$ from the diagram), then $m\angle BFC = 90 - 27=61^{\circ}$.

Step4: Find $m\angle BFE$

Since $\angle BFA = 39^{\circ}$ and $\angle AFE = 180^{\circ}$ (straight - angle), then $m\angle BFE=180 - 39 = 141^{\circ}$.

Answer:

• Set of complementary angles: $\angle BFA$ and $\angle DFE$
• Set of supplementary angles: $\angle AFB$ and $\angle BFE$
• $m\angle DFE = 53^{\circ}$
• $m\angle BFC= 61^{\circ}$
• $m\angle BFE = 141^{\circ}$