Answer:
x = 65° and y = 32.5°
Step-by-step explanation:
In Δ ABC,
m∠A + m∠B + m∠C = 180° (Sum of angles of a triangle)
50° + x + x = 180° (∵ AB = AC angels opposite to equal sides of triangle are equal)
2x = 180° - 50° = 130°
x = 130°/2 = 65°
Now, Since ∠ACB is the exterior angle of triangle ADC,
∴ ∠CAD + ∠ADC = ∠ACB (An exterior angle of a triangle is equal to the sum of its opposite interior angles)
y + y = 65° (∵ AC = CD angels opposite to equal sides of triangle are equal)
2y = 65°
y = 65/2 = 32.5°
