let x, y and z represent the measurements of the angles of the triangle and x < y < z

since they are angles in triangle their sum is equal to 180 degrees:

x + y + z = 180

the smallest angle of a triangle is 1/3 the measurement of the largest, and 20° less than the other angle

x = (1/3)z

x = y - 20

by solving the system of equations

x + y + z = 180

x = (1/3)z

x = y - 20

we find

x = 32 degrees

y = 52 degrees

z = 96 degrees

click here to see the step by step solution of the system of equations

the angles of the triangle are 32, 42 and 96 degrees.