Question

1. 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 and
m∠dfe = 90 - 27 = 63
set of supplementary angles
∠afb and ∠bfe
m∠bfc = 180 - 79 = 101
m∠bfe = 180 - 79 = 101

Explanation:

Step1: Recall angle - sum properties

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

Step2: Identify complementary angles

If one angle is $27^{\circ}$, its complement $\angle DFE$ is $90 - 27$.

Step3: Identify supplementary angles

$\angle AFE$ and $\angle BFE$ form a linear pair. Given $\angle AFB = 30^{\circ}$ and $\angle BFO = 79^{\circ}$, find $m\angle AFE$ and $m\angle BFE$ using the $180^{\circ}$ sum property for supplementary angles.

Answer:

Set of complementary angles: $\angle DFE$ and some angle with measure $27^{\circ}$ (assuming one of the small - angled pairs sums to $90^{\circ}$), $m\angle DFE = 90 - 27=63^{\circ}$; Set of supplementary angles: $\angle AFE$ and $\angle BFE$, $m\angle AFE = 180 - 30 = 150^{\circ}$, $m\angle BFE=180 - 79 = 101^{\circ}$