Final answer:
In a quadrilateral, the sum of two angles is 160 degrees. The other two angles are in the ratio 2:3. The measures of the angles in the ratio 2:3 are 8 degrees and 12 degrees.
Step-by-step explanation:
In a quadrilateral, the sum of two interior angles is always 180 degrees, just like in a triangle. So if we have a quadrilateral with two angles adding up to 160 degrees, the other two angles must add up to 180 - 160 = 20 degrees.
Let's call the first angle in the ratio 2:3 as 2x and the second angle as 3x.
According to the given ratio, 2x + 3x = 20. Combining like terms, we get 5x = 20. Dividing both sides by 5, we find x = 4.
Therefore, the measures of the angles in the ratio 2:3 are 2x = 2(4) = 8 degrees and 3x = 3(4) = 12 degrees.