#1: $90/$27 = x/6, so by cross multiplying, 6(90) = 27x. 540 = 27x, dividing both sides by 27 gives x = 20.

#2: If you continue line segment A to intersect m, then opposite interior angles are formed, which are congruent. Since there are 180 degrees in a triangle, you know that the third (and supplemental angle to x) must be (180 - 30 - 50) = 100. So, since x is supplemental to 100, it must be 80 degrees.

#3a) Continue the line that forms the 40 degree angle, so that it intersects the other of the parallel lines ( I am assuming the top and bottom lines are parallel). It will form a triangle that includes angle x. We know that the supplemental angle to 60 must be 120. So the three angles forming the triangle are 120 + x + 40, since 40 is an opposite interior angle. So, x must be 20 degrees, since there are 180 in a triangle.