Answer:
∠DCA ≅ 56°
Reason: vertical angles theorem
∠DCF ≅ 144°
Reason: Angles on a straight line (DE) add up to 180°
∠ECB ≅ = 37°
Reason: Angles on a straight line (FA) add up to 180°
∠CAB ≅ ∠DCA ≅ 56°
Reason: Alternate interior angles theorem
∠CBA ≅ ∠ECB ≅ 37°
Reason: Alternate interior angles theorem
Step-by-step explanation:
∠DCA ≅ ∠ECF ≅ 56°
Reason: vertical angles theorem
∠DCF ≅ 180 - 56 = 144°
Reason: Angles on a straight line (DE) add up to 180°
∠ECB ≅ 180 - 56 - 87 = 37°
Reason: Angles on a straight line (FA) add up to 180°
∠CAB ≅ ∠DCA ≅ 56°
Reason: Alternate interior angles theorem
∠CBA ≅ ∠ECB ≅ 37°
Reason: Alternate interior angles theorem
