Complementary Angles Definitions and Examples
Complementary Angles
In mathematics, a complementary angle is an angle that is the reciprocal of another angle. The two angles are said to be complementary if the sum of their angles is 180 degrees.
There are many examples of complementary angles in everyday life. For example, if you stand on one foot and extend your arm out to the side, your arm makes a right angle with your body. Your other leg forms a 90 degree angle with your torso, so your total angle looks like an acute triangle. If you turn your head to look at the opposite side of this triangle (and move your arms back to their original positions), you’ll see that your right and left hands now form complimentary angles – they’re both pointing outwards from the centerline of your body at 45 degrees.
Complementary angles can also be found in geometric shapes. A right triangle has two acute angles – one at each vertex – and one complimentary angle between them; similarly, a square has four 90 degree angles, two at each corner.
What are Complementary Angles?
Complementary angles are angles that are both acute and right angles. They are important in geometry, especially when creating shapes such as triangles and quadrilaterals. When two angles are complementary, the larger angle is divided by the smaller angle to create a new angle. Complementary angles can also be created using formulas or algebra.
There are many examples of complementary angles throughout geometry. For example, in a right triangle, the two acute angles are complementary because they share a equal measure (90 degrees). The other example is in a quadrilateral where each pair of opposite sides is complementary.
Complementary Angles Definition
In mathematics, complementary angles are two angles that are not supplementary. The sum of the two angles is 180 degrees. Complementary angles always form pairs, with one angle in each pair being complementary to the other angle.
There are many definitions of complementary angles, but here are a few examples:
Theorem 1: If ABC is a right triangle and AC is adjacent to BC, then AC is complementary to BA.
Theorem 2: If A is inside of B and C is outside of B, then A and C are complementary angles.
Theorem 3: If D is a line segment perpendicular to AB and AE is a line segment parallel to AB that passes through D, then AD and BE are complementary angles.
Adjacent Complementary Angles
Adjacent complementary angles are angles that are adjacent to one another on the circumference of a circle. The two angles that make up an adjacent complementary angle are called the angle’s complement (or hypotenuse).
An example of an adjacent complementary angle is 120 degrees, which is formed by the two angles at the vertices of a right triangle: 90 degrees at the base and 30 degrees at the hypotenuse.
How to Find Complement of an Angle?
In geometry, a complement of an angle is the measure of the angle’s difference from 180 degrees. Complementary angles are important in plane and heliocentric trigonometry, as well as in surveying and land management.
To find the complement of an angle, divide the angle by 2. For example: the complement of 150 degrees is 75 degrees.
Properties of Complementary Angles
What are complementary angles?
A pair of angles that are opposite each other on the coordinate plane (x, y) are said to be complementary. The sum of the two angles is 180 degrees, so they are also called supplementary angles. Complementary angles can be identified by their locations on the coordinate plane and by their exterior/interior angles.
There are four types of complementary angles: interior, exterior, right, and left. These correspond to pairs of corresponding angle properties: right angle, 90 degrees; interior angle, 0 degrees; exterior angle, 90 degrees; and left angle, 270 degrees.
The exterior angle property is the most important because it determines how a pair of complementary angles compares in size. For example, if you have a 90-degree exterior angle and an interior angle of 0 degrees, then their combined size is 180 degrees—a right angle. But if you instead have a left exterior angle of 270 degrees and an interior angle of 90 degrees, then their combined size is 360 degrees—an isoceles triangle! In other words, the left exterior Angle creates twice as much space as the right exterior Angle does. The same holds true for all other combinations of complementary angles: create any two complementary angles and you’ll get another right angle.
So what do these angles have to do with one another?
As mentioned earlier, when two complementary angles share an edge one another they create a right angle.
Complementary Angles and Supplementary Angles
There are two types of angles: complementary angles and supplementary angles. Complementary angles are pairs of angles that are opposite one another in a right triangle. For example, the angle formed by the base and the hypotenuse is a complementary angle because it is opposite the angle formed by the other two sides. Supplementary angles are any other type of angle apart from complementary angles.
Supplementary angles can be divided into three categories based on their relationship to other angles: adjacent, interior, and exterior. Adjacent supplementary angles are adjacent to one another, while interior supplementary angles are within the same polygon as one another but not adjacent to one another. Exterior supplementary angles are outside of any polygon.
Examples of supplementary angles include the following:
The sum of two adjacent supplementary angles is 180 degrees.
The sum of an interior and exterior supplementary angle is 270 degrees.
The sum of two exterior supplementary angles is 360 degrees.
Complementary Angles Theorem
The complementary angles theorem states that two angles are complementary if they have the same measure (angle subtended by each side). In other words, they are inversely proportional to each other.
Complementary angles can be used to create simple geometric shapes, like a right triangle or an isosceles triangle. They also play an important role in trigonometry and other mathematical disciplines.
Here are some examples of how the theorem can be used:
If you want to create a right triangle with one acute angle and one obtuse angle, you need to find the complement of the obtuse angle. To do this, take the square root of both sides: This gives you your complementary angle, which is 135 degrees.
Complementary Angles Examples
The complementary angles are two angles that are opposite one another. Together, they form a right angle. Complementary angles can be found in mathematics and trigonometry, but they can also be seen in everyday life.
Let’s look at an example of how complementary angles can be used in everyday life. Suppose you want to build a wall using straight lines. You would start by drawing a line that is perpendicular to the ground. Then, you would draw another line that is parallel to the first line but at a different height. The two lines will intersect at the height of your desired wall, forming a right angle.
Practice Questions on Complementary Angles
What are complementary angles?
Angles are two angles that share a common measure. Angles are complimentary if the sum of their measures is 180 degrees. Angles can be measured in radians or degrees.
We can think of complementary angles as working together to create a shape. For example, when we look at a right angle, we see that its two sides are always equal. If we were to fold one of those sides in on itself, it would create a 90-degree angle. In other words, the side that was originally straight is now curved and has created another angle – this new angle is complementary to the original 90-degree angle.
When measuring complementary angles, we use the same method as working with whole numbers (addition and subtraction). The first angle is called the vertex of the complementary triangle and the second angle is called the opposite vertex. The sum of the measures of these two angles is always 180 degrees (aka 360 degrees).
Conclusion
In this article, we explore the term “complementary angles.” We discuss what it means and provide examples of how it can be used in geometry. This information is essential if you want to be able to understand and use other terms related to complementary angles. After reading this article, you should have a better understanding of what these angles are and how they work together. Be sure to continue exploring them by studying additional resources!
