A triangular playground has angles with measures in the ration 8:4:6. What is the measure of the smallest angle?(1 point)

27 degrees
30 degrees
40 degrees
80 degrees

1 answer

The ratio of the angle measures in a triangle is equal to the ratio of the corresponding side lengths. Let's denote the angle measures as 8x, 4x, and 6x.

The sum of the angle measures in a triangle is always 180 degrees. So, we have:

8x + 4x + 6x = 180
18x = 180
x = 10

Therefore, the angles measure:

8x = 8 * 10 = 80 degrees
4x = 4 * 10 = 40 degrees
6x = 6 * 10 = 60 degrees

So, the smallest angle measures 40 degrees.

Therefore, the answer is 40 degrees.