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. ${60}^{\circ }$
• C. ${65}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is A

${58}^{\circ }$

Let one of the complementary angles be $x^{\circ }$.

Then second angle = $2x^{\circ }-6^{\circ }$ [Since, second angle is 6 less than twice the first]

Then, $\left(x\right)+(2x-6^{\circ })={90}^{\circ }$

$\Rightarrow 3x={96}^{\circ }$

$\Rightarrow x={32}^{\circ }$

First angle = ${32}^{\circ }$

Second angle = $2x-6^{\circ }=2\left({32}^{\circ }\right)-6^{\circ }={64}^{\circ }-6^{\circ }={58}^{\circ }$

$\Rightarrow$ The larger angle is ${58}^{\circ }$.