Final answer:
To find the angle measures of a triangle with a given ratio, solve an equation to find the value of x. Then, multiply x by the corresponding numbers given in the ratio to find the measures of the angles.
Step-by-step explanation:
To find the angles of a triangle with a given ratio, we need to find the measures of each angle. Let's say the ratio is 1:3:5. We can assume that the smallest angle has a measure of 1x, the second angle has a measure of 3x, and the largest angle has a measure of 5x.
Since the sum of the angles of a triangle is 180 degrees, we have the equation 1x + 3x + 5x = 180. Simplifying, we get 9x = 180. Dividing both sides by 9, we find that x = 20.
So, the measures of the angles are 20 degrees, 60 degrees, and 100 degrees.