The measures of the angles of LMN are in the ratio 1:2:5. what are the measurements of the angles

I assume LMN here refers to a triangle, in which case we know that its interior angles have to add to 180°. What this ratio is saying is that, if we split that 180 up into some number of pieces, one of the angles is going to take up 1 of those pieces, one is going to take up 2 pieces, and one is going to take up 5 pieces. How many pieces did we split the 180 up into the first place? Adding up all of the pieces, we find that the number is 1 + 2 + 5 = 8.

Splitting 180 up 8 ways makes the value of each piece 180 : 8 = 22.5, so the measures of our angles are

1 * 22.5 = 22.5°, 2 * 22.5 = 45°, and 5 * 22.5 = 112.5°