Question

Two angles are complementary. One angle is $80\%$ of the other angle. The two angles are

• A. ${10}^{\circ },{80}^{\circ }$
• B. ${20}^{\circ },{70}^{\circ }$
• C. ${30}^{\circ },{60}^{\circ }$
• D. ${50}^{\circ },{40}^{\circ }$

Answer 1

Answer: (D)

${50}^{\circ },{40}^{\circ }$

Let one angle be $x$.

Then, the other angle $=\frac{80}{100}\times x=0.8x$.

Given the angles are complementary

$\therefore x+0.8x={90}^{\circ }$

$\Rightarrow 1.8x={90}^{\circ }$

$\Rightarrow x=\frac{90^{\circ }}{1.8}=50^{\circ }$.

Hence, the angles are:

$\Rightarrow x=1\times 50^{\circ }={50}^{\circ }$

$\Rightarrow 0.8x=0.8\times 50^{\circ }=40^{\circ }$.

Hence, option $D$ is correct.