Two supplementary angles are such that one is 14 times larger than the other. Find the two angles. (Enter solutions from smallest to largest.)
let x = first angle
let 180-x = second angle
then we set up the equation,
14x = 180-x
14x + x = 180
15x = 180
x = 12 degrees
180-x = 168 degrees
hope this helps~ :)
To solve this problem, we need to understand the concept of supplementary angles. Supplementary angles are a pair of angles that add up to 180 degrees.
Let's assume that the smaller angle is x degrees. According to the problem, the larger angle is 14 times larger than the smaller angle, so it would be 14x degrees.
Since the sum of the two angles is 180 degrees, we can set up the equation:
x + 14x = 180
Combining like terms, we get:
15x = 180
To solve for x, we divide both sides of the equation by 15:
x = 180 / 15
x = 12
Therefore, the smaller angle is 12 degrees, and the larger angle is 14 times larger, so it is:
14x = 14 * 12 = 168 degrees
Hence, the two angles are 12 degrees and 168 degrees.