A quadrilateral has two angles that measure 310° and 15°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?

First, we need to know that the sum of all angles in a quadrilateral is 360°.

Given two angles are 310° and 15°, we can find the sum of these two angles:

310° + 15° = 325°

Subtract this from the total 360° to find the sum of the remaining two angles:

360° - 325° = 35°

The problem states that the remaining two angles are in a ratio of 3:4. This means the two angles can be represented as 3x and 4x, where x is a common factor.

Since the sum of these two angles is 35°, we can set up the equation:

3x + 4x = 35

Solving for x gives:

x = 35 / 7 = 5

Therefore, the measures of the two remaining angles are:

3x = 3 * 5 = 15° 4x = 4 * 5 = 20°

So, the measures of the two remaining angles are 15° and 20°.