Question

The measures of two complementary angles are

12q−9
and
8q+14
Find the measures of the angles.

Answer 1

4 1/4

Explanation:

Complementary angles add up to 90 degrees.

Thus if 12q - 9 and 8q + 14 are complementary,

12q - 9 + 8q + 14 = 90.

Combining like terms, we get:

20q + 5 = 90

20q = 85

Thus, q = 85/20, or 17/4, or 4 1/4

Answer 2

42 and 48

Explanation:

∵ Two angles are complementary to each other if their sum is 90°,

Given,

12q - 9 and 8q + 14 are complementary angles,

By the above statement,

12q - 9 + 8q + 14 = 90

Combine like terms,

20q + 5 = 90

Subtract both sides by 5,

20q = 85

Divide both sides by 20,

q = 4.25,

Thus, the angles are,

12(4.25) - 9 and 8(4.25) + 14

⇒ 42 and 48