The measures of the angles of triangle LMN are in the ratio 1:2:5. What are the measures of the angles?

If the angles are in this order: L:M:N = 1:2:5

Let Angle l = x, then angle M = 2x and angle N = 5x

The summation of the angles is 180 degrees. That is,

x+2x+5x = 180 = > 8x=180 = > x (that is angle L) = 180/8 = 22.5°

Angle M = 2x = 2*22.5 = 45°

Angle N = 5x = 5*22.5 = 112.5°

The angles of the triangle are 22.5°, 45° and 112.5°