ClassX Video Lessons Subjects Algebra Complementary and supplementary angles | Angles and intersecting lines | Geometry
In geometry, angles are super important for understanding shapes and how they work. Let’s dive into the world of angles and learn about adjacent, complementary, and supplementary angles with some easy examples!
Imagine we have two angles: angle ABC and angle DBA.
For our example, let’s say:
Angles ABC and DBA share a side, which is ray BA. When two angles share a side, they are called adjacent angles. This means they are right next to each other!
We can figure out the measure of angle DBC by adding angles DBA and ABC together:
Since angle DBC is 90 degrees, it’s a right angle.
When two angles add up to 90 degrees, they are called complementary angles. In our example, angles DBA and ABC are complementary because:
Also, when lines or rays form a right angle, they are called perpendicular. So, line segment DB is perpendicular to line segment BC.
Now, let’s talk about supplementary angles. Imagine two angles, angle XYZ and angle MNO, where:
Adding these angles gives us:
When two angles add up to 180 degrees, they are called supplementary angles.
If two supplementary angles are also adjacent, they share a side. For example, if angle DBA is 50 degrees and angle ABC is 130 degrees, then:
This means angles DBA and ABC are both supplementary and adjacent. Together, they form a straight angle, which is 180 degrees.
Understanding these angle concepts is a big step in learning geometry and helps you tackle more complex problems later on!
Using a protractor and ruler, draw different pairs of angles on a piece of paper. Label them and measure their degrees. Try to create examples of adjacent, complementary, and supplementary angles. Share your drawings with the class and explain which type of angles you have drawn and why.
Go on an angle hunt around your classroom or home. Look for real-life examples of adjacent, complementary, and supplementary angles. Take pictures or make sketches of your findings. Present your discoveries to the class and explain how each example fits into the angle categories.
Work in pairs to solve angle puzzles. Your teacher will provide you with a set of angle problems where you need to find missing angles using the concepts of adjacent, complementary, and supplementary angles. Discuss your strategies with your partner and check your answers together.
Use an online geometry tool or app to explore angles. Adjust the angles to see how they change from being complementary to supplementary. Challenge yourself to create specific angle measures and test your understanding by predicting the outcomes before adjusting the angles.
Create a short story or comic strip that involves characters who are angles. Use the concepts of adjacent, complementary, and supplementary angles in your story. Share your story with the class and explain how the angle concepts are integrated into your narrative.
Angles – An angle is formed when two rays meet at a common endpoint. – The angles in a triangle always add up to 180 degrees.
Adjacent – Adjacent angles are two angles that have a common side and a common vertex. – In the diagram, angle A and angle B are adjacent because they share a side.
Complementary – Complementary angles are two angles whose measures add up to 90 degrees. – If one angle is 30 degrees, its complementary angle is 60 degrees.
Supplementary – Supplementary angles are two angles whose measures add up to 180 degrees. – The two angles on a straight line are supplementary because they add up to 180 degrees.
Measure – The measure of an angle is the size of the angle in degrees. – The measure of angle C is 45 degrees.
Degrees – Degrees are the units used to measure angles. – A right angle is exactly 90 degrees.
Right – A right angle is an angle that measures exactly 90 degrees. – The corner of a square forms a right angle.
Perpendicular – Two lines are perpendicular if they intersect to form right angles. – The lines on the graph are perpendicular to each other.
Vertex – A vertex is the point where two or more lines or edges meet. – The vertex of the angle is the point where the two rays meet.
Shapes – Shapes are the forms of objects, defined by their boundaries or surfaces. – Triangles, squares, and circles are all different types of shapes.
