Question

Two angles are complementary. One angle's measure is 3 more than 9

times the other angle. What is the measure of each angle? Write each
angle's measure separately. ​

Answer 1

The measure of one angle is 81.3° and the other angle is 8.7°.

Explanation:

We are given that two angles are complementary. One angle's measure is 3 more than 9 times the other angle.

Let the measure of one angle be 'x' and the measure of other angle be 'y'.

So, according to the question;

• The first condition states that two angles are complementary, this means that the sum of both angles must be equal to 90°, i.e;

x + y = 90°

x = 90° - y ---------------- [equation 1]

• The second condition states that One angle's measure is 3 more than 9 times the other angle, i.e;

x = 3 + 9y ------------ [equation 2]

Now, both the equations we get;

90 - y = 3 + 9y

9y + y = 90 - 3

10y = 87

`y=(87)/(10)` = 8.7°

Now, putting the value of y in equation 1 we get;

x = 90° - y

x = 90° - 8.7° = 81.3°

Hence, the measure of one angle is 81.3° and the other angle is 8.7°.