Question

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

set of supplementary angles

m∠dfe=

m∠bfc=

m∠bfe=

Explanation:

Step1: Define complementary angles

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

Step2: Define supplementary angles

Supplementary angles sum to $180^{\circ}$.

Step3: Calculate $m\angle DFE$

$m\angle DFE=m\angle DFC - m\angle CFE$, assume $m\angle DFC = 90^{\circ},m\angle CFE = 27^{\circ}$.

Step4: Calculate $m\angle BFC$

$m\angle BFC = 180 - m\angle AFB$, assume $m\angle AFB=79^{\circ}$.

Step5: Calculate $m\angle BFE$

$m\angle BFE=180 - m\angle AFB$, assume $m\angle AFB = 79^{\circ}$.

Answer:

• Set of complementary angles: $\angle DFE$ and $\angle CFE$ (assuming $\angle DFC = 90^{\circ}$)
• Set of supplementary angles: $\angle AFB$ and $\angle BFE$ (assuming $A - F - E$ are collinear)
• $m\angle DFE$: Assume $\angle DFC = 90^{\circ}$ and $\angle CFE = 27^{\circ}$, then $m\angle DFE=90 - 27=63^{\circ}$
• $m\angle BFC$: If $\angle AFB = 79^{\circ}$ and assuming $\angle AFC = 180^{\circ}$, then $m\angle BFC=180 - 79 = 101^{\circ}$
• $m\angle BFE$: If $\angle AFB = 79^{\circ}$ and $A - F - E$ are collinear, then $m\angle BFE = 180-79=101^{\circ}$