Question

One of the 2 complementary angles is 6 less than twice the other.

Find the measure of the larger angle.

• A. ${58}^{\circ }$
• B. ${38}^{\circ }$
• C. ${32}^{\circ }$
• D. ${52}^{\circ }$

Answer 1

The correct option is A

${58}^{\circ }$

Let the complementary angles be $x^{\circ }and(90-x{)}^{\circ }$

$\Rightarrow x=2(90-x)-6$

$\Rightarrow x=180-2x-6$

$\Rightarrow x+2x=180-6$

$\Rightarrow 3x=174$

$\Rightarrow x=58$

$\Rightarrow (90-x)=90-58=32°$

$\therefore Largerangle={58}^{\circ }$