To solve this, first look at the information we're given. We know that the shape the missing angle is part of is a triangle, so therefore, the sum of the interior angles will always be 180 degrees. There is a right angle inside of the triangle. One of the exterior angles is 132 degrees.
The first thing we can see from this is that the two interior angles which are not right angles must add up to 90 degrees. Since the sum of all the interior angles is 180 degrees, and there is already a 90 degree angle, the other two must add up to 90 degrees. The next step would then be to find the other interior angle which is not the missing angle. We can do this because of the exterior angle. A straight line always has a measure of 180 degrees. In this case, we can see that the line the exterior angle is resting on is straight, and the exterior angle + the other interior angle = the line. Therefore, 132 + the other interior angle must equal 180 degrees. Subtract 132 from both sides, and you get the other interior angle has a measure of 48 degrees. Now, to take that and figure out the missing angle. We know that the angle with a measure of 48 degrees and the missing angle must add up to 90 degrees, as stated above. 48 + missing angle = 90 Subtract 48 from both sides, and you get the measurement of the missing angle is 42 degrees.
