the angles of a certain quadrilateral are in the ratio 2:3:4:6. calculate the size of the largest angle

Sure, here are the steps to solve the problem:

1. First, understand that the sum of all angles in any quadrilateral is 360 degrees.

2. The problem states that the angles of the quadrilateral are in the ratio 2:3:4:6. Add these ratios together to get a total. 2 + 3 + 4 + 6 = 15.

3. To find the size of each angle, you would divide the total degrees of a quadrilateral (360 degrees) by the total of the ratios (15). So, 360/15 = 24 degrees. This means that each "part" of the ratio is equal to 24 degrees.

4. The largest angle is represented by the ratio 6. So, to find the size of the largest angle, multiply this ratio by the size of each part. So, 6 * 24 = 144 degrees.

So, the size of the largest angle in the quadrilateral is 144 degrees.