Intersecting lines have three important properties.
First, the interior angles formed by intersecting lines form a circle, so the sum of these angles is 360 degrees, or 360°. In the diagram shown, a + b + c + d = 360.
Second, interior angles that combine to form a line sum to 180°. These are termed supplementary angles. Thus, in the same diagram shown, a + d = 180, because angles a and d form a line together. Other supplementary angles are b + c = 180, a + c = 180, and d + b = 180.
Third, angles found opposite each other where these two lines intersect are equal. These are called vertical angles. Thus, in the previous diagram, a = b, because these angles are opposite one another and are formed from the same two lines. Additionally, c = d for the same reason.
Note that these rules apply to more than two lines that intersect at a point, as shown to the right. In this diagram, a + b + c + d + e + f = 360, because these angles combine to form a circle. In addition, a + b + c = 180, because these three angles combine to form a line. Finally, a = d, b = e, and c = f, because they are pairs of vertical angles.
If b + f = 150, what is d?
What is x − y?
