Question

Recall that two angles are complementary if the sum of their measures is​ 90°. Find the measures of two complementary angles if one angle is two times the other angle.

Answer 1

Answer: 30 and 60 degrees

Explanation:

Let the angles be x and 2x.

So x + 2x = 90

3x = 90

x = 30

So the measures are 30 and 60 degrees

Answer 2

The measures of the angles are :

↬ 30

↬ 60

Solution:

Let's call one angle
`y`. Then, two times y is
`\sf{2y}`.

Now, we know that if the sum of the measures of the angles is​ 90° then they are complementary.

So we can form an equation using the info:

• 
  `\sf{2y+y=90}`

Combine like terms

`\sf{3y=90}`

Divide each side by 3.

`\sf{y=30}`

That was y. We also need to find 2y.

So I plug in 30 for y : 2y = 2(30) = 60

Hence, one angle is 30° and the other one is 60°.

Note that these two angles are indeed complementary, because they add to 90 perfectly.