Question 969745
35 and 50 degrees  ANSWER

The interior angles of a quadrilateral measure to 360 degrees

Two of them are known and are 167 and 108.  They add to 275 degrees.

The other two angles must sum to (360-275)=85 degrees.

They are in a ratio of 7:10

The sum of these two numbers is 17, and (85/17)=5

So 5 * (7:10) will be 35:50, keeping the same ratio balance.

The other two angles are 35 and 50 degrees respectively.

The sum of all 4 angles is 360 degrees.

Note, with a 7:10 ratio, you could also just start with 7 and 10 degrees, then 14 and 20 degrees then 21 and 30 degrees until you reached 35 and 50 degrees.  If you can recognize that the sum of the numbers in the ratio is a factor of the number of degrees you need, then the (85/17) is faster.  Simply doubling, tripling, etc. of the ratio will get you to the answer, too.