Which angles form an adjacent pair

They share a vertex and side, but do not overlap. Vertical angles are not adjacent. The line through points A, B and C is a straight line. There are some special relationships between "pairs" of angles.

A Linear Pair is two adjacent angles whose non-common sides form opposite rays. If two angles form a linear pair, the angles are supplementary. When two lines intersect, the angles opposite to each other are equal and are called vertical angles or vertically opposite angles. Each angle is called the complement of the other angle.

It is not necessary that the angles must always be adjacent to each other, as in the case of linear pairs. In other words, all linear pairs are supplementary, but all supplementary angles need not be linear pairs.

When two angles are supplementary angles each angle is called the supplement of the other angle. When 2 parallel lines are cut by a transversal, many pairs of angles are formed. These pair of angles have a special relationship between them. Let us discuss the pairs of angles formed by a transversal in detail. When a transversal intersects two parallel lines, the co-interior angles are always supplementary. Co-interior angles are those angles that:.

Therefore, they are supplementary. When a transversal intersects two parallel lines , the alternate interior angles formed are always equal. Alternate-interior angles are those angles that:. When a transversal intersects two parallel lines, the alternate exterior angles formed are always equal. Alternate-exterior angles are those angles that:. When a transversal intersects two parallel lines, the corresponding angles formed are always equal. Corresponding angles are the angles that:. Vertically opposite angles are technically not adjacent angles, but where you find adjacent angles, you will likely also find some vertically opposite angles.

Vertical angles have already been explored, but to clarify, vertical angles share the same vertex but do not share any of the same sides. If we take the above picture, 3 and 4 and 1 and 2 are considered vertically opposite angles. A key property of vertically opposite angles is that they measure exactly the same. For example, if angle 1 was 30 degrees, angle 2 would also measure as 30 degrees. Put simply, adjacent angles are angles that share a common side and a common vertex corner point.

This is TRUE in some cases! Supplementary adjacent angles always add up to This is because the two angles sit next to each other on a straight line and all angles on a straight line add up to However, if the adjacent angles are not linear pairs and another angle is in the mix, the two adjacent angles will not add up to As vertical and adjacent angles can often exist in a small area together, many people believe that vertical angles can also be adjacent angles.

Vertical angles do not share any of the same sides, meaning they cannot be adjacent. Adjacent angles can be linear pairs. As linear pairs share both a common side and a common vertex, they can be considered adjacent angles. However, not all adjacent angles are linear pairs. This was a quick run through of adjacent angles to help you get to grips with this integral part of the geometry syllabus.