1. Geometry Chapter 1
Section 1-4
Measuring 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. Ray BA and BC are two non-collinear rays
What Is An Angle ?
When two non-collinear rays join with a common endpoint (origin) an angle is formed. A
Ray BA B
Common endpoint B C
Ray BC
Common endpoint is called the vertex of the angle. B is the vertex of ÐABC.
Ray BA and BC are two non-collinear rays
Ray BA and ray BC are called the sides of ÐABC.

4. If we look around us, we will see angles everywhere.
Angles In Daily Life
If we look around us, we will see angles everywhere.

5. 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 1
For example: ÐABC or ÐCBA
We may also name this angle only by the single letter of the vertex, for example ÐB or by a number.

6. Interior And Exterior Of An Angle
An angle divides the points on the plane into three regions:
Points lying on the angle (An angle) A B C P T X F R
Points within the angle (Its interior portion. )
Points outside the angle (Its exterior portion. )

7. Measurement Of An Angle
One way to measure and angle is in degrees. To indicate the size or degree of an angle write a lower case m in front of the angle symbol.
The measure of angle B is 65 degrees You show this by writing
m<B = 65. A B C

8. Measurement Of An Angle Protractor is used to measure and draw angles.
Angles are accurately measured in degrees.

9. 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

10. Right angle: An angle whose measure is 90 degrees.
Straight Angle
Right Angle
Acute Angle
Obtuse Angle

11. Examples Of Right Angle

12. Obtuse angle: An angle whose measure is greater than 90 degrees.
Straight Angle
Right Angle
Acute Angle
Obtuse Angle

13. Examples Of Obtuse Angle

14. Acute angle: An angle whose measure is less than 90 degrees.
Straight Angle
Right Angle
Acute Angle
Obtuse Angle

15. Examples Of Acute Angle

16. Straight angle: An angle whose measure is 180 degrees.
Right Angle
Acute Angle
Obtuse Angle

17. Examples Of Straight Angle

18. Greater than a right angle
Which of the angles below is a right angle, less than a right angle and greater than a right angle? 1. D E F 2. P Q R
Test Yourself 1
Greater than a right angle A B C
Right angle 3.
Less than a right angle

19. 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.

20. Pairs Of Angles : Types Adjacent angles Linear pairs of angles
Vertical Angles
Complimentary angles
Supplementary angles

21. Adjacent angles do not overlap each other.
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 ÐABD and ÐDBC
ÐABC and ÐDEF are not adjacent angles
Adjacent angles do not overlap each other.

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

23. Vertical Angle Pairs 1 2 4 3 ∠1 and ∠3 ∠4 and ∠2
Vertical Angles: two angles whose sides are opposite rays. 1 2 4 3
Name the pairs of vertical angles.
∠1 and ∠ ∠4 and ∠2

24. Pairs Of Angles : Types
Complimentary angles
Supplementary angles

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

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

27. 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

28. 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

29. Test Yourself 2 ÐABD and ÐDBC ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC
Name the adjacent angles and 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 pair of angles:
ÐEBA, ÐABC
ÐEBD, ÐDBC

30. Pairs Of Angles
Your Turn
Complete problems on
Page 72-73
#18 -25

31. Modified by Mrs. D. Joseph Excerpts The Department of Research
The End
Modified by Mrs. D. Joseph
Excerpts The Department of Research
Bombay Cambridge Gurukul

32. Contents Recap the terms Test Yourself - 1 Angles in daily life
Congruent angles
Pairs of angles: Types
What is an angle?
Test Yourself - 2
Naming an angle
Pairs of angles formed by a transversal
Interior and exterior of an angle
Measurement of angle
Test Yourself - 3
Types of angle: Right angle
Obtuse angle
Acute angle
Straight angle