Two complementary angles are in the ratio of 4:6. Find the measure of the smallest angle.

Question

what is the value of x?

Answer 1

Hi Maya,

Two complementary angles have a sum of 90 degrees.

You can use a pair of equivalent ratios to solve this problem. Since 90 is the sum of the two angles, we can use the ratio of 4 : 6 and write it as a part - to - whole ratio where 10 is the whole (the total of the two angles in the given ratio);

4 = x

10 90

We can solve for x (the smaller of the two angles) by multiplying the numerator and denominator by 9:

4 • 9 = x

10 • 9 90

x = 36°

The other angle will be 90- 36= 54°

Note that 36 = 4

54 6