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~ :)
Well, let's call the smaller angle x. According to the problem, the larger angle is 14 times larger, so it would be 14x. Since they are supplementary angles, their sum would be 180 degrees.
So, we can set up the equation: x + 14x = 180.
Simplifying that, we get: 15x = 180.
Dividing both sides by 15, we find: x = 12.
So the smaller angle is 12 degrees, and the larger angle would be 14 times larger, which is 14 * 12 = 168 degrees.
So the two angles are 12 degrees and 168 degrees.
Let's represent the smaller angle as x.
According to the given information, the larger angle is 14 times larger than the smaller angle. Therefore, the larger angle is 14x.
Supplementary angles add up to 180 degrees. So, we can set up the equation:
x + 14x = 180
Combining like terms:
15x = 180
To isolate x, we can divide both sides of the equation by 15:
x = 180/15
Simplifying:
x = 12
Now we can find the larger angle by substituting the value of x into the expression for the larger angle:
14x = 14 * 12
Calculating:
14x = 168
Therefore, the two angles are 12 degrees and 168 degrees.
To find the two angles, we can set up a system of equations based on the given information. Let's denote the measure of the smaller angle as x degrees.
According to the problem, the larger angle is 14 times larger than the smaller angle. Therefore, the measure of the larger angle is 14x degrees.
We also know that two supplementary angles add up to 180 degrees. So, we can write the equation:
x + 14x = 180
Now, let's solve this equation to find the value of x:
15x = 180
Dividing both sides by 15:
x = 12
So, the measure of the smaller angle is 12 degrees.
Now, we can find the measure of the larger angle by substituting the value of x into the expression we derived earlier:
14x = 14 * 12 = 168
Therefore, the two angles are 12 degrees and 168 degrees.