Question

The degree measure of one of two complementary angles is twice that of the other. What is one of the degree measures of the angles?

A.) 30 degrees
B.)40 degrees
C.)45 degrees
D.)27 degree

Answer 1

Question :

The degree measure of one of two complementary angles is twice that of the other. What is one of the degree measures of the angles?

Answer :

A.) 30 degrees

Solution :

Let one angle = x

According to statement,

Another angle = 2 × first angle

`\sf : \implies Another \: angle = 2x`

Now, we know that sum of complementary angles is 90°

Hence,

`\sf : \implies x + 2x = 90^(\circ)`

`\sf : \implies 3x = 90^(\circ)`

`\sf : \implies x = \frac{\cancel{90}^(\circ)}{\cancel{3}}`

`\sf : \implies x = 30^(\circ)`

`\Large \underline{\boxed{\sf{ x = 30^(\circ) }}}`

Therefore, one of the angle is 30°.

Another angle = 2 × 30° = 60°

Answer 2

30° is one of the degree measures of the angles.

Hence, option (A) is true.

Explanation:

• Let 'x' be the degree measure of the first angle.

Given that the degree measure of one of two complementary angles is twice that of the other.

• Thus, the other angle = 2x

Complementary angles

• We know that two angles are termed as complementary angles when the sum of their measured angles is 90°.

Thus the equation becomes

x + 2x = 90°

3x = 90°

Divide both equations by 3

3x/3 = 90°/3

x = 30°

Therefore, 30° is one of the degree measures of the angles.

Hence, option (A) is true.