The ratio of the angles in a quadrilateral are 2:3:5:10, what is the measure of the largest angle?

180 deg, but this situation cannot exist (see below)

Step-by-step explanation:

The sum of the measures of the angles of a quadrilateral is

(n - 2) 180 = (4 - 2) 180 = 2 (180) = 360

Since the measures of the angles are in the ratio 2:3:5:10, multiplying all of those numbers by the same number will give 4 angle measures also in that ratio. We don't know what number to multiply by to get the actual measures of this quadrilateral, so we call that number x.

The measures are 2x, 3x, 5x, and 10x.

We add the measures and set the sum equal to 360. Then we solve for x.

2x + 3x + 5x + 10x = 360

20x = 360

x = 18

The largest angle measures 10x = 10 * 18 = 180 degrees.

This means this quadrilateral does not exist. A polygon cannot have an interior angle measuring 180 degrees.

Are you sure the numbers in the ratio are correct?