The sum of the measures of the angles of any triangle is 180. In a particular triangle, one angle is 40 greater than the smallest angle, and the third angle is 10 less than three times the smallest angle. Find the measure of the three angles.

The smallest angle is 30 degrees, the second angle is 80 degrees and the third angle is 70 degrees

Step-by-step explanation:

let x = the smallest angle

This means that one angle is x+40, and the third angle is 3x-10. This make our equation:

x + 40 + 3x - 10 + x = 180

Combine like terms

5x + 30 = 180

Subtract 30 from both sides

5x = 150

Divide both sides by 5

x = 30

Plugging this in:

3x - 10 =

90 - 10 =

80

And for the other:

x + 40 =

30 + 40 =

70

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2