Question

The measure of an angle is fourteen times the measure of a complementary angle. What is the measure of each angle?

°
and
°

Answer 1

The measures of the two complementary angles are 6 degrees and 84 degrees, with the larger angle being fourteen times the measure of the smaller one.

Step-by-step explanation:

To solve this problem, let's use algebra. Let the smaller angle be x degrees. Since the angles are complementary, their sum is 90 degrees. The larger angle is given as fourteen times the smaller one, so it can be represented as 14x degrees. We can set up the following equation:

x + 14x = 90

Solving for x gives:

15x = 90

x = 90 / 15

x = 6

Therefore, the smaller angle measures 6 degrees, and the larger angle, being fourteen times greater, measures 84 degrees (14 * 6 = 84).

Answer 2

Answer:
`6^(\circ)` and
`84^(\circ)`

Step-by-step explanation:

Let x be the measure of the angle ( in degrees), the measure of its complementary will be 14x.

We know that the sum of two complementary angles is 90°.

According to the question , we have

`x+14x=90\\\\\Rightarrow\ 15x=90\\\\\Rightarrow\ x=(90)/(15)=6`

Hence, the measure of angle is
`6^(\circ)` and its complementary is
`14(6)=84^(\circ)`