We are asked to find the measure of angle 5 in the image.
Analysing the image, we see that it consists of two parallel lines that are being intercepted by another line. In the points at which the slant line intercepts the parallel pair of lines, we know that the angles formed are equal in the following fashion:
angle 1 equals angle 5 (alternate angles between parallel lines)
angle 7 equals the angle marked with measure 70 degrees (again because by construction they are alternate angles among parallel lines)
of course it also happens that angle 2 equals angle 6, and angle 4 equals angle 8, but we don't need in oarticular these las pairs of angles to answer the question. we just need the first two pairs mentioned above that I am marking as bold now.
we also recall that the angles that added form a straight line, are called "supplementary angles", and added must give 180 degrees (the straight line).
Then, we know that angle 1 plus angle 70 degrees (in the upper portion of the drawing), must add to 180 degrees.
SInce one is 70 degrees, then angle 1 must be 180 - 70 = 110 degrees
So we know that angle 1 measures 110 degrees.
We now recall that we have mentioned that angles 1 and 5 must be equal for being alternate angles between parallel lines, so we conclude that angle 5 is 110 degrees.