Answer:
∠A = 70°, ∠B = 50°, and ∠C = 60°.
Step-by-step explanation:
In a triangle ΔABC, ∠A + ∠B + ∠C = 180° ......... (1), we know from the property of triangle.
Now, the sum of ∠C and the exterior angle adjacent to ∠C is 180°.
If the exterior angle adjacent to ∠C is 120°, then ∠C = 180° - 120° = 60°.
Now, from equation (1), ∠A + ∠B = 180° - ∠C = 180° - 60° = 120° ......... (2)
Now, given that ∠A = 2x and ∠B = x + 15.
Hence, from equation (2), we have, 2x + x + 15 = 120
⇒ 3x = 105
⇒ x = 35.
Therefore, ∠A = 2x = 2 × 35 = 70°
∠B = x + 15 = 35 + 15 = 50°
and ∠C = 60° (Answer)
