1. Types of Angles

2. Recap Geometrical Terms
An exact location on a plane is called a point.
Point
A straight path on a plane, extending in both directions with no endpoints, is called a line.
Line
A part of a line that has two endpoints and thus has a definite length is called a line segment.
Line segment
A line segment extended indefinitely in one direction is called a ray.
Ray

3. What Is An Angle ?
When two rays join with a common endpoint (vertex) an angle is formed. A
Ray BA B
Common endpoint B C
Ray BC
Ray BA and BC are two rays
Common endpoint is called the vertex of the angle. B is the vertex of ÐABC.
Ray BA and ray BC are called the arms of ABC.

4. Naming An Angle A B C For example: ÐABC or ÐCBA
To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. A B C
For example: ÐABC or ÐCBA
We may also name this angle only by the single letter of the vertex, for example ÐB.

5. Measurement Of An Angle
A protractor is used to measure and draw angles.
Angles are accurately measured in degrees.

6. There are four main types of angles.
Right angle
Acute angle
Obtuse angle A B C A B C A B C
Straight angle B A C

7. Right angle: An angle whose measure is 90 degrees.

8. Obtuse angle: An angle whose measure is greater than 90 degrees.

9. Acute angle: An angle whose measure is less than 90 degrees.

10. Straight angle: An angle whose measure is 180 degrees.

11. Test Yourself 1 1. D E F 2. P Q R A B C 3.
Which of the angles below is a right angle, an obtuse angle, and an acute angle? 1. D E F 2. P Q R
Test Yourself 1
Obtuse Angle A B C
Right Angle 3.
Acute Angle

12. Pairs Of Angles : Types Adjacent Angles Vertical Angles
Congruent Angles
Adjacent Angles
Vertical Angles
Complementary Angles
Supplementary Angles
Linear Angles

13. Congruent Angles A B C D E F D E F
Two angles that have the same measure are called congruent angles. A B C
300 D E F
300 D E F
300
Congruent angles have the same size and shape.

14. Adjacent Angles ABC and DEF are not adjacent angles
Two angles that have a common vertex and a common ray are called adjacent angles. C D B A
Common ray
Common vertex D E F A B C
Adjacent Angles ABD and DBC
ABC and DEF are not adjacent angles
Adjacent angles do not overlap each other.

15. Vertical Angles ÐAPC = ÐBPD ÐAPB = ÐCPD
Vertical angles are pairs of angles formed by two lines intersecting at a point. A D B C
ÐAPC = ÐBPD P
ÐAPB = ÐCPD
Four angles are formed at the point of intersection.
Vertical angles are congruent.
Point of intersection ‘P’ is the common vertex of the four angles.

16. ÐABC and ÐDEF are complementary because
Complementary Angles
If the sum of two angles is 900, then they are called complementary angles.
600 A B C
300 D E F
ÐABC and ÐDEF are complementary because
ÐABC + ÐDEF
= 900

17. ÐDEF and ÐPQR are not complementary because
Contd….
If the sum of two angles is more than 900 or less than 900, then are they not complementary angles.
700 D E F
300 p Q R
ÐDEF and ÐPQR are not complementary because
ÐDEF + ÐPQR
= 1000

18. ÐPQR and ÐABC are supplementary, because
Supplementary Angles
If the sum of two angles is 1800 then they are called supplementary angles. R Q P A B C
1000
800
ÐPQR and ÐABC are supplementary, because
ÐPQR + ÐABC
= 1800

19. ÐDEF and ÐPQR are not supplementary because
Contd….
If the sum of two angles is more than or less than 1800, then they are not supplementary angles. C B A
1100 D E F
800
ÐDEF and ÐPQR are not supplementary because
ÐABC + ÐDEF
= 1900

20. Two adjacent supplementary angles are called linear angles.
1200
600 C D P
ÐAPC + ÐAPD
= 1800

21. ÐABD and ÐDBC Test Yourself 2 ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC
Name a pair of adjacent angles and a linear pair of angles in the given figure:
Adjacent angles: C D B A E
600
300
900 C D B A E
600
300
900
ÐABD and ÐDBC
ÐABE and ÐDBA
Test Yourself 2
Linear angles:
ÐEBA, ÐABC
ÐEBD, ÐDBC

22. Adjacent angles: ÐAPC and ÐCPD
Name a pair vertical angles and a pair of adjacent angles in the given figure: A D B C P
Adjacent angles: ÐAPC and ÐCPD
Vertical angles: ÐAPC and ÐBPD
ÐAPB and ÐBPD
ÐAPB and ÐCPD

23. The End