Question

Find

Answer 1

The measures of two complementary angles are 64 degrees and 26 degrees

Solution:

Let the larger angle be "a" and smaller angle be "b"

Two angles are Complementary when they add up to 90 degrees

so we get,

a + b = 90 ------ eqn 1

Given that measure of the larger angle is 12 more than twice the measure of the smaller angle

larger angle = 12 + 2(smaller angle)

a = 12 + 2b --- eqn 2

Let us solve eqn 1 and eqn 2 to get values of "a" and "b"

Substitute eqn 2 in eqn 1

12 + 2b + b = 90

12 + 3b = 90

3b = 90 - 12

3b = 78

b = 26

Therefore from eqn 2,

a = 12 + 2b

a = 12 + 2(26)

a = 12 + 52

a = 64

Thus the measures of two complementary angles are 64 degrees and 26 degrees