Question

If 4∠A = 2∠B = ∠C, ∠A and ∠B are complementary angles and ∠B and ∠C are supplementary angles, then the measures of ∠A, ∠B and ∠C are, respectively

• A. 22°, 44°, 88°
• B. 30°, 60°, 120°
• C. 40°, 80°, 100°
• D. 120°, 60°, 30°

Answer 1

The correct option is B 30°, 60°, 120°

Given: 4∠A = 2∠B = ∠C
Since ∠A and ∠B are complementary angles.
$\therefore \angle A+\angle B={90}^o$ …..(i)
$\Rightarrow \angle A+2\angle A={90}^o$ (∵ 4∠A = 2∠B)
$\Rightarrow \angle A=\frac{{90}^o}{3}={30}^o$
From (i), we get
${30}^o+\angle B={90}^o$
$\Rightarrow \angle B={60}^o$ …..(ii)
Also, ∠B and ∠C are supplementary angles.
$\therefore \angle B+\angle C={180}^o$
$\Rightarrow {60}^o+\angle C={180}^o$ [From (ii)]
$\Rightarrow \angle C={120}^o$
Therefore, the measures of ∠A, ∠B and ∠C are ${30}^o,{60}^o$ and ${120}^o$ respectively.
Hence, the correct answer is option (b).