Question

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Explanation:

Step1: Read angles from protractor

• $m\angle AFC$: Ray FA aligns with 0, FC aligns with 130, so $m\angle AFC = 130^\circ$
• $m\angle CFB$: Ray FB aligns with 50, FC aligns with 130, so $m\angle CFB = 130^\circ - 50^\circ = 80^\circ$
• $m\angle AFD$: Ray FA aligns with 0, FD aligns with 140, so $m\angle AFD = 140^\circ$
• $m\angle EFC$: Ray FE aligns with 180, FC aligns with 130, so $m\angle EFC = 180^\circ - 130^\circ = 50^\circ$

Step2: Find supplementary angles (sum to $180^\circ$)

• For $\angle AFB$ ($50^\circ$): $180^\circ - 50^\circ = 130^\circ$, so pair with $\angle AFD$
• For $\angle AFC$ ($130^\circ$): $180^\circ - 130^\circ = 50^\circ$, so pair with $\angle AFB$
• For $\angle AFD$ ($140^\circ$): $180^\circ - 140^\circ = 40^\circ$, so pair with $\angle DFE$

Step3: Find complementary angles (sum to $90^\circ$)

• For $\angle BFC$ ($80^\circ$): $90^\circ - 80^\circ = 10^\circ$, so pair with $\angle DFE$
• For $\angle AFB$ ($50^\circ$): $90^\circ - 50^\circ = 40^\circ$, so pair with $\angle DFE$

Step4: Solve supplementary angle pair A&B

$m\angle B = 180^\circ - 38^\circ = 142^\circ$

Step5: Solve complementary angle pair C&D

$m\angle D = 90^\circ - 20.5^\circ = 69.5^\circ$

Answer:

1.
A. $130^\circ$
B. $80^\circ$
C. $140^\circ$
D. $50^\circ$

2.
$\angle AFB$ and $\angle AFD$
$\angle AFC$ and $\angle AFB$
$\angle AFD$ and $\angle DFE$

3.
$\angle BFC$ and $\angle DFE$
$\angle AFB$ and $\angle DFE$

1. $142^\circ$

1. $69.5^\circ$