Two angles of a quadrilateral measure 227° and 87°. The other two angles are in a ratio of 11:12. What are the measures of those two angles?

Question

Two angles of a quadrilateral measure 227° and 87°. The other two angles are in a ratio of 11:12. What are the measures of those two angles? Please help I dont have time

Answer 1

Here's how to do a similar problem. Suppose the 2 angles were 30 and 130 degrees, and the other 2 angles were in a ratio of 3:7. If 2 numbers are in the ratio 3:7, then they must be equal to 3x and 7x for some value of x. Since there are 360 degrees in a quadrilateral, we must have

30 + 130 + 3x + 7x = 360

160 + 10x = 360

10x = 200

x = 20

So the other 2 angles must be 60 and 140 degrees.

Answer 2

The sum of the angles of a quadrilateral is 360°.

The remaining two angles account for 46°

11/(12+11)=11/23=x/46 => x = 22°

and the other angle is 24° (i.e. 46-22).