A quadrilateral has two angles that measure 31° and 249°. The other two angles are in a ratio of 3:17. What are the measures of those two angles?

Step-by-step explanation:

Given 1st angle = 31° and 2nd angle = 249°

Let the remaining two angles be 3x and 17x

31° + 249° + 3x + 17x = 360°

280° + 20x = 360°

20x = 360° - 280°

20x = 80°

Therefore x = 4°

Now

Measurements of both angles

3x = 3 * 4° = 12°

17x = 17*4° = 68°

Step-by-step explanation:

We first need to find the measure of the other 2 angles. The angles of a quadrilateral all add up to equl 360, so:

360 - 249 - 31 = 80

The other 2 angles add up to equal 80 degrees. If these angles exist in a 3:17 ratio, then algebraically,

3x + 17x = 80 and

20x = 80 so

x = 4. That means that one angle is 3 (4) = 12 and the other angle is 17 (4) = 68.

249 + 31 + 12 + 68 = 360.