Question

each row in the table below shows one possible set of angle measurements for this drawing. use the drawing and the given angle measurement to find the missing angle measurements. angle afb angle bfc angle dfe angle efa 48 42 48 132 36 140

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle AFB$ and $\angle DFE$ are vertical angles.

Step2: Identify complementary - angles

$\angle BFC$ and $\angle AFB$ are complementary since $\angle AFC = 90^{\circ}$. So $\angle BFC=90^{\circ}-\angle AFB$.

Step3: Identify supplementary - angles

$\angle EFA$ and $\angle AFB$ are supplementary since they form a straight - line. So $\angle EFA = 180^{\circ}-\angle AFB$.

For the row with $\angle DFE = 36^{\circ}$:

Step4: Find $\angle AFB$

Since $\angle AFB=\angle DFE$ (vertical angles), $\angle AFB = 36^{\circ}$.

Step5: Find $\angle BFC$

$\angle BFC=90 - 36=54^{\circ}$ (complementary angles).

Step6: Find $\angle EFA$

$\angle EFA=180 - 36 = 144^{\circ}$ (supplementary angles).

For the row with $\angle EFA = 140^{\circ}$:

Step7: Find $\angle AFB$

$\angle AFB=180 - 140=40^{\circ}$ (supplementary angles).

Step8: Find $\angle BFC$

$\angle BFC=90 - 40 = 50^{\circ}$ (complementary angles).

Step9: Find $\angle DFE$

$\angle DFE=\angle AFB = 40^{\circ}$ (vertical angles).

angle AFB	angle BFC	angle DFE	angle EFA
40	50	40	140

Answer:

angle AFB	angle BFC	angle DFE	angle EFA
40	50	40	140