Question

A and B are complementary. If A four times larger than B, what is the measure of each angle?A. 69° and 21°B. 65° and 22°C. 70° and 20°D. 18°and 72°

Answer 1

Complementary angles

Two angles are complementary when the sum of their measures is equal to 90°. Then if we have an angle with a measure of x° and another with a measure of y° and they are complementary we get the following:

`x+y=90`

Measures of A and B

We are told that A and B are complementary which means that their measures meet the following equation:

`A+B=90`

We also know that A is four times larger than B so we get:

`A=4B`

Then if we replace A with 4B in the first equation we get:

`\begin{gathered} 4B+B=90 \\ 5B=90 \end{gathered}`

Then we divide both sides by 5:

`\begin{gathered} (5B)/(5)=(90)/(5) \\ B=18 \end{gathered}`

Then, if B is 18° A must be:

`A=4B=4\cdot18=72`

So A=72°. Then the answer is option D.