Question

Help with this geometry problem

Answer 1

∠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

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