In a ΔABC, side BC is extended to a point D. The exterior angle at C is 105°. The interior angles at A and B are in the ratio 2 : 5. What is the measure of the largest interior angle of the triangle?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 75°.
Exterior angle at C = 105°, ∠A : ∠B = 2 : 5
Exterior angle = ∠A + ∠B = 105°
Let ∠A = 2k, ∠B = 5k
⇒ A + B = 2k + 5k = 7k = 105°
⇒ k = 105°/7 = 15°
Largest inrerior angle = 5 × 15° = 75°