Answer:
Step-by-step explanation:
Angle ABC is the sum of angles ABD and DBC as per angle addition postulate
As per given we have isosceles triangles ABD and BCD
ADC is straight angle, therefore:
- 2x + x = 180°
- 3x = 180°
- x = 60°
Triangle ABD
- ∠BAD = ∠ABD = 1/2(180° - 2x) = 1/2(180° - 120°) = 1/2(60°) = 30°
Triangle BCD
- ∠BDC =∠ BCD = x = 60°
- ∠DBC = 180° - 2*60° = 180° - 120° = 60°
So the angle ABC
- ∠ABC = ∠ABD + ∠DBC
- ∠ABC = 30° + 60° = 90°
