In the figure above, E is a point on line segment AD. If 70 < a < 80, what are the possible integer values of b?

Solution:

The possible integer values of b are101, 102, 103, 104, 105, 106, 107, 108, 109.

Since, angles a and b lie on the same line, the angles are supplementary (angles on a line)

Therefore, a + b = 180.

Now we are given that 70 < a < 80.

Or 70 + b  < a + b < 80 + b

Or 70 + b < 180  < 80 + b

Or 100 < b < 110

Therefore, the possible integer values of b are101, 102, 103, 104, 105, 106, 107, 108, 109.