In the diagram shown above, we see triangle ABC and the dotted line through A that is parallel to BC. Since angle A, from the triangle, and angles 1 and 2 form a straight (dotted) line, the sum of their measures is 180º. We also know that since the dotted line is parallel to BC that by alternate interior angles. This gives us: Substituting for angles 1 and 2 we have This result is true for all triangles:
We have 34º + 72º = 106º. Therefore the third angle has a measure of 180º - 106º = 74º
180º - 106º = 74º
We must have Collecting like terms and solving gives us: This gives us: Notice the following: 35.92º + 57.3º + 86.76º = 179.98º The reason that this does not add up to exactly 180º is because we rounded off in calculating the value of x.