Question

Find the measure of an angle, if four times of its complement is ${12}^o$ more than twice the difference between its supplement and complement.

• A. $36$
• B. $45$
• C. $42$
• D. $24$

Answer 1

Answer: (C)

$42$

Two angles whose sum is ${180}^o$ are said to be supplementary.

Two angles whose sum is ${90}^o$ are said to be complementary.

Let the angle be $x$.

Given that $4(90-x)=2[(180-x)-(90-x)]+12$

$\Rightarrow 360-4x=2\times 90+12$

$\Rightarrow 360-4x=180+12\Rightarrow 360-4x=192$

$\Rightarrow 4x=360-192$

$\Rightarrow 4x=168$

$\Rightarrow x=\frac{168}{4}$

$\Rightarrow x=42$

Therefore, the angle is ${42}^o$.