Question

Determine the measure of an angle whose measure is 14 times that of its complement

If two angles of a triangle are complementary, what is the measure of the angle?

Answer 1

84°

Explanation:

Let the two complementary angles be x and y.

If the measure of an angle is 14 times the other, then x = 14y...... 1

Since the two angles are complementary, their sum will be 90° i.e x+y = 90° ...... 2

Substitute equation 1 into 2

14y+y = 90

15y = 90

y = 90/15

y = 6

Since the angle is x = 14y

x = 14(6)

x = 84°

Hence the measure of the angle is 84°