To solve this problem, we have to set up an equation using the ratio and our knowledge that the sum of the three inside angles of a triangle must be 180 degrees, as follows:
3x + 8x + 9x = 180
To simplify this equation, we have to combine like terms on the left side of the equation, so we get the equation:
20x = 180
Finally, we must divide the left side of the equation by 20 to get the variable x alone.
x=9
Now, we must use the ratio to find the measures of the three angles.
3x = 3(9) = 27
8x = 8(9) = 72
9x = 9(9) = 81
We can verify that our answer is correct because the three angle measures add up to 180 degrees.
Therefore, the smallest angle is 27 degrees, the medium angle is 72 degrees, and the biggest angle is 81 degrees.
Hope this helps!