Answer: 148°
Step-by-step explanation:
BA ≅ CA, ∠CBA = 2x, ∠BCA = 3x - 8 Given
∠CBA = ∠BCA Definition of congruency
2x = 3x - 8 Substitution
-x = -8 Subtraction Property of Equality
x = 8 Division Property of Equality
∠CBA = 2(8) Substitution
∠CBA = 16 Simplify
∠BCA = 16 Transitive Property
∠CBA + ∠BCA + ∠BAC = 180° Triangle Sum Theorem
16 + 16 + ∠BAC = 180° Substitution
32 + ∠BAC = 180° Simplify
∠BAC = 148° Subtraction Property of Equality
∠BAC ≅ ∠DAE Vertical Angle Theorem
∠BAC = ∠DAE Definition of congruency
∠DAE = 148° Transitive Property
