Complementary &Supplementary Angles.pptx

complementary and supplementary

1. COMPLEMENTARY AND SUPPLEMENTARY ANGLES

2. RECALL WHAT WE DISCUSSED YESTERDAY

3. THE ANGLE QUEST

4. THE ANGLE QUEST I n the vibrant kingdom of Geometria, there lived two young angles named Compli and Suppli. Compli, the complementary angle, was always cheerful and content, while Suppli, the supplementary angle, was serious and focused .

5. THE ANGLE QUEST One sunny day, King Geome asked them to embark on a quest to solve a mysterious problem that had been troubling the kingdom. They had to find the missing piece to complete a puzzle—a perfect square.

6. THE ANGLE QUEST The catch was that the missing angle could either be complementary or supplementary to the known angle. As they journeyed through valleys and over mountains, they encountered various challenges, testing their knowledge of angles and geometry.

7. THE ANGLE QUEST Along the way, they met a wise old sage who presented them with their first question: Sage: “Dear travelers, can you tell me the relationship between complementary and supplementary angles?”

8. THE ANGLE QUEST Compli: “Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees.” Suppli: “Indeed, Compli is correct. It’s all about the sum of angles!”

9. THE ANGLE QUEST Impressed by their knowledge, the sage bestowed upon them a clue to their quest: “Look to the stars for guidance.” As night fell, they gazed up at the celestial canopy, searching for clues among the twinkling stars.

10. THE ANGLE QUEST Suddenly, they noticed two constellations—one forming a right angle, and the other a straight angle. Compli: “Could it be that the missing angle is complementary to one and supplementary to the other?”

11. THE ANGLE QUEST Suppli: “Yes, let’s test our theory!” With renewed determination, they returned to the kingdom and placed the missing angle in the puzzle.

12. THE ANGLE QUEST To their delight, it fit perfectly, completing the square. King Geome congratulated them on their success and asked one final question: King Geome: “How did you determine the missing angle?”

13. THE ANGLE QUEST Compli: “We observed the relationships between complementary and supplementary angles, as well as the clues from the stars.” Suppli: “And through collaboration and critical thinking, we were able to solve the puzzle.”

14. THE ANGLE QUEST And so, Compli and Suppli became heroes of Geometria, their tale forever remembered as a testament to the power of knowledge and teamwork.

15. 1. What is the difference between complementary and supplementary angles, according to Compli and Suppli? According to Compli and Suppli, complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees.

16. 2. How did Compli and Suppli use their knowledge of angles and the clue from the stars to solve the puzzle? Compli and Suppli observed the relationships between complementary and supplementary angles, as well as the clues from the stars, to determine that the missing angle could be complementary to one angle and supplementary to the other. They used this knowledge to successfully solve the puzzle.

17. WHAT IS COMPLEMENTARY ANGLE? WHAT IS SUPPLEMENTARY ANGLE?

18. COMPLEMENTARY ANGLES In geometry, complementary angles are defined as two angles whose sum is 90 degrees. In other words, two angles that add up to 90 degrees are known as complementary angles.

19. COMPLEMENTARY ANGLES For example : I f angle A is 20 degrees, then its complement angle B would be 70 degrees because 20 degrees + 70 degrees = 90 degrees.

20. COMPLEMENTARY ANGLES In this case, 20 degrees and 70 degrees are complements of each other. 20 degrees is the complement of 70 degrees 70 degrees is the complement of 20 degrees

21. COMPLEMENTARY ANGLES ∠ 1 + ∠ 2 = 90° 60° + 30° = 90° 60° is the complement of 30° 30° is the complement of 60°

22. Types of Complementary Angles Adjacent Complementary Angle s Non-adjacent Complementary Angles

23. 1. Adjacent Complementary Angles Two complementary angles with a common vertex and a common arm /side are called adjacent complementary angles.

24. Adjacent Complementary Angles ∠COB & ∠AOB are adjacent angles as they have a common vertex "O" and a common arm /side "OB". They also add up to 90 degrees, that is ∠COB + ∠AOB = 70° + 20° = 90°.

25. 2. Non-a djacent Complementary Angles Two complementary angles that are NOT adjacent are said to be non-adjacent complementary angles.

26. 2. Non-a djacent Complementary Angles ∠ABC and ∠PQR are non-adjacent angles as they neither have a common vertex nor a common arm /side ∠ABC + ∠PQR = 50° + 40° = 90°

27. How to Find Complement of an Angle? 90-x° Example: Find the complement of 37 ° Solution: Let the required angle be x. Then its complement is (90 ° - x). It is given that: angle = its complement x = 90 ° - 37 ° x = 53 ° Thus, the angle which is equal to its complement is 45 ° .

28. SUPPLEMENTARY ANGLES Supplementary angles refer to the pair of angles that always sum up to 180°. Supplementary angles form a straight angle (180°) when they are put together. Therefore, these two angles are called supplements of each other.

29. Supplementary Angles ∠ 1 + ∠ 2 = 180 ° ∠ 13 0° + 5 0° = 18 0°

30. Supplementary Angles T here are two types of supplementary angles. Adjacent supplementary angles Non-adjacent supplementary angles

31. Adjacent Supplementary Angles Two supplementary angles with a common vertex and a common arm are said to be adjacent supplementary angles. ∠COB and ∠AOB are adjacent angles as they have a common vertex , O ∠COB + ∠ AOB = 70° + 110° = 180°

32. Non-a djacent Supplementary Angles Angles that may add up to 180° but they do not share any common vertex or common arm. ∠ABC and ∠PQR are non-adjacent angles as they neither have a common vertex nor a common arm . ∠ABC+ ∠PQR = 79° + 101° = 180°

33. How to Find the Sup plement of an Angle? 18 ° -x° Example: Find the supplement of 86° Solution: The supplement of 86° is obtained by subtracting it from 180°. This means 180° - 86° = 94°. Therefore, the supplement of 77° is 103° .

34. Determine whether the following angles are complementary.

35. Determine whether the following angles are supplementary.

36. 1 . The complement of 65 ° is _____. 2 . The complement of 50 ° is _____. 3 . The supplement of 10 0° is _____. 4 . The supplement of 80° is _____. Write the complement (items 1-2) and supplement (items 3-4) of each angle given below.

37. ANGLE ∠1 ∠2 Complementary 40 ° 1) ______ Supplementary 2) ______ 90 ° Complementary 3) ______ 45 ° Supplementary 150 ° 4) ______ 5) ____________ 1 ° 179 ° COMPLETE THE TABLE BELOW. For 5 minutes .

38. TIME’S UP! LET US ANSWER!

39. ANGLE ∠1 ∠2 Complementary 40 ° 1) 50 ° Supplementary 2) 90 ° 90 ° Complementary 3) 45 ° 45 ° Supplementary 150 ° 4) 30 ° 5) Supplementary 1 ° 179 ° COMPLETE THE TABLE BELOW.

40. 1. Two angles are complementary if they add up to 90°. 2. Two angles are supplementary if they add up to 180°. 3. The angle that is equal to its complement is 45°. 4. The angle that is equal to its supplement is 90°.

41. ASSIGNMENT: Definition of: congruent angles vertical angles adjacent angles linear pairs perpendicular lines parallel lines intersecting lines

42. Thank you for listening