Final answer:
To find the measures of the three angles of a triangle when they are in the ratio 1:3:5, assign variables for the angles, set up an equation, solve for x, and substitute the value back into the ratios to find the measures of the angles. The triangle is acute.
Step-by-step explanation:
To find the measures of the three angles of a triangle when they are in the ratio 1:3:5, we can start by assigning variables. Let's say the measures of the angles are x, 3x, and 5x. Since the sum of the angles in a triangle is 180 degrees, we can set up the equation x + 3x + 5x = 180. Combining like terms, we get 9x = 180. Dividing both sides by 9, we find x = 20.
Now, we can substitute this value back into the ratios to find the measures of the angles. The first angle is x, so it would be 20 degrees, the second angle is 3x, so it would be 60 degrees, and the third angle is 5x, so it would be 100 degrees.
Therefore, the measures of the angles in the given triangle are 20 degrees, 60 degrees, and 100 degrees. Since all angles are less than 90 degrees, this triangle is classified as an acute triangle.