In a triangle, the measure of the first angle is twice the measure of the second angle. the measure of the 3rd angle is 68 degrees more than the measure of the 2nd angle. use the fact that the sum of the measures of the 3 angles of a triangle is 180 degrees to find the measure of each angle. what is the measure of the smallest angle?

To give every angle a label:

First angle = 2x
Second angle = x
Third angle = x + 68
So, because the sum of the interior angles of the triangle is 180°, we can say that: 2x + x + (x + 68) = 180

2x + x + x = 4x

4x + 68 = 180

Isolating for x we get: x = (180-68)/4 x = 28

Because the first angle is twice as large and the third angle is greater than the second angle, the measure of the smallest angle is 28°.