if the angles of a triangles with measures in the ratio 5:6:7, then find the measure of the smallest angles.
Let the measures of the angles be 5x, 6x, and 7x, respectively.
Since the sum of the angles in a triangle is 180 degrees, we have:
5x + 6x + 7x = 180
18x = 180
x = 10
Therefore, the measures of the angles are:
Smallest angle: 5x = 5(10) = 50 degrees. Answer: \boxed{50}.