Answer:
24°
Explanation:
Let x = one complementary angle
Let y = the other complementary angle
As the sum of two complementary angles is 90°:
x + y = 90
If one angle is 18° more than two times the other angle:
y = 18 + 2x
Rewrite x + y = 90 to make x the subject:
x = 90 - y
Now substitute x = 90 - y into y = 18 + 2x and solve for y:
y = 18 + 2(90 - y)
⇒ y = 18 + 180 - 2y
⇒ 3y = 198
⇒ y = 198 ÷ 3 = 66
Now substitute found value of y = 66 into x + y = 90 and solve for x:
x + 66 = 90
⇒ x = 90 - 66 = 24
Therefore, the larger angle = 66° and the smaller angle = 24°