To calculate the angles of a quadrilateral when given the ratio of their measures, follow these steps:

Step 1: Sum the ratios to find the total number of parts.

2 + 5 + 4 + 1 = 12

Step 2: Calculate the value of each part.

360 degrees (sum of angles in a quadrilateral) / 12 (total number of parts) = 30 degrees per part

Step 3: Multiply each part by the corresponding ratio to find the measure of each angle.

2 parts * 30 degrees = 60 degrees

5 parts * 30 degrees = 150 degrees

4 parts * 30 degrees = 120 degrees

1 part * 30 degrees = 30 degrees

Therefore, the angles of the quadrilateral are:

60 degrees, 150 degrees, 120 degrees, and 30 degrees.