When we talk about angles in geometry, we talk about angles between lines (also known as lines of measure). That is, if two lines are parallel, their angle is either 0 or 180 degrees. And if they’re not parallel, their angle is between 0 degrees to 180 degrees. Thus, the two angles are said to be adjacent angles when they share the common vertex and side. The endpoints of the ray from the side of an angle are called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side. An arc is simply the vertical segment of a line passing through the center. A segment that passes through a point on the opposite side of the line segment is also considered an arc. Adjacent arcs are lines that share the same side and center.
To find which adjacent angles are complementary and supplementary look at the symmetry operations defined by angle symmetry. When the sum of the adjacent angles is 90 degrees then they are called complementary angles. But, if the sum of the adjacent angles is 180 degrees then they are called supplementary angles.
Properties of Adjacent Angles
Adjacent angles have some important properties that can be used while solving problems. Below are some of the important properties of adjacent angles.
- They have a side in common.
- They have a vertex in common.
- The angles do not cross one other or in other words, overlap.
- Although they share a common side in the middle, they do not share the other side.
- They don’t have a common point on the inside.
- They might be either complementary or supplemental.
Real-Life Examples of Adjacent Angles
- Crossroads-Sometimes two or more roads intersect at the same point in two different planes. Two roads intersect at a point, in two different planes, hence the adjacent angle. In this case, the intersection point of the roads can be called the intersection point of the perpendicular. Often we can combine adjacent angles to form an asymmetric triangle. In some cases, such as when the angles are exactly 90 degrees, it is called the right-angle case. The intersecting angle of a right angle triangle is the directrix of the triangle, which is always the square with the long side directly above the short side.
- Steering Wheel of a Car- The steering wheel of a car is the perfect example of an adjacent angle. If the steering wheel of a car is a three-spoke unit then it forms an adjacent angle. The three spokes of the steering can be placed at any angle. Sometimes they may also form a supplementary angle i.e. the sum of the angles formed by the three spokes of the steering is equal to 180 degrees.
- Three Hands of a Clock- This is one of the most relatable examples. Everyone must have seen a clock and also the three hands i.e. the hour hand, the minute’s hand, and the second’s hand. At any given instant they form an adjacent angle. The three hands of a clock can form both complementary and supplementary angles. For instance, if the hour hand is at 12, the minute hand is at 3, and the second hand is anywhere between 12 and 3, then this forms a complementary adjacent angle. The sum of the angles formed by the three hands in this configuration is always going to be 90 degrees. Also, if the hour hand is at 12, the minute hand is at 6, and the second hand is anywhere between 12 and 6, then this forms a supplementary adjacent angle. The sum of the angles formed by the three hands in this configuration is always going to be 180 degrees.
Thus, adjacent angles have played an important role in the transformation of geometry. They have helped in giving many more concepts like alternate interior angles, supplementary and complementary angles, etc. To get a better understanding of adjacent angles visit Cuemath. They have explained all the concepts in the best way possible.
