When two lines cross each other, they form four angles at the point of intersection. Among these angles, two pairs of vertical angles are created. Vertical angles are the angles that are opposite each other when two lines intersect. For example, if we label the angles formed as A, B, C, and D, where A and C are one pair of vertical angles, and B and D are the second pair, we can observe the following:
Each pair of vertical angles is equal; that is, angle A is equal to angle C, and angle B is equal to angle D. Therefore, if angle A measures 50 degrees, angle C will also measure 50 degrees. This reasoning holds true for angles B and D as well.
Now, to find the sum of all four angles formed (A, B, C, D), we can note that:
- Angle A + Angle B + Angle C + Angle D = 180 degrees (because a straight line measures 180 degrees).
- Thus, in a complete rotation around the intersecting point, the total measures of the angles combined yield:
- 180 degrees (from angle A and B) + 180 degrees (from angle C and D) = 360 degrees.
Conclusively, the sum of all four angles formed when two lines intersect is 360 degrees.