In a ΔABC; 8∠A = 6∠B = 3∠C. What are the degree measures of ∠A, ∠B, and ∠C?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 36°, 48°, 96°.
Let 8∠A = 6∠B = 3∠C = k
∠A = k/8; ∠B = k/6; and ∠C = k/3
The sum of angles in a triangle is 180°.
∠A + ∠B + ∠C = 180°
⇒ (k/8) + (k/6) + (k/3) = 180°
⇒ 15k/24 = 180°
⇒ k = (180° × 24)/15 = 288°
∠A = k/8 = 288°/8 = 36°
∠B = k/6 = 288°/6 = 48°
∠C = k/3 = 288°/3 = 96°
Therefore, the degree measures of the angles are 36°, 48°, and 96°.