Question

The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.

Answer 1

Measure of first angle = 65° and Measure of second angle = 35°

Explanation:

Let measure of first angle be a and measure of second angle be b

Now, the measure of the first angle is 15 less than twice the measure of the second angle

⇒ a + 15 = 2b

⇒ a = 2b - 15

Now, sum of two complementary angles is 90

⇒ a + b = 90

⇒ 2b - 15 + b = 90

⇒ 3b - 15 = 90

⇒ 3b = 105

⇒ b = 35

And a = 65

Therefore, Measure of first angle = 65° and Measure of second angle = 35°

Answer 2

let 2nd angle = x

then 1st angle = 2x-15

then you have 90 = x + 2x-15

2x +x = 3x

so now 90 = 3x-15

add 15 to each side

105=3x

x = 105/3 = 35

1st angle = 35 degrees

2nd angle = 2(35) - 15 = 70-15 = 65