This document defines and describes different types of angles: - Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees but less than 180 degrees. Right angles are 90 degrees. Straight angles are 180 degrees. Reflex angles are greater than 180 degrees but less than 360 degrees. - Angles can be calculated based on their relationship to other angles, such as angles around a point adding up to 360 degrees and angles on a straight line adding up to 180 degrees. Vertically opposite angles are always equal. - When parallel lines are intersected by a transversal, the corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of the transversal are

1. Introduction
Angles In Daily Life
Basic Terms And Definitions
Parallel Lines And A Transversal
Types of Angles
Properties of Angles
-

2. SECTION 1
Introduction
What do we know about angles?
Where can we see angles in everyday
life?
 An angle is formed when two lines meet and is
measured in degrees.
 We use a little circle ° following the number to
mean degrees.
 For example 54° means 54 degrees

3. Angles in daily
life
Angles in daily life
If we look around us, we will see angles everywhere.

4. TYPES OF ANGLES
1) Acute angle
2) Right angle
3) Obtuse angle
4) Straight angle
5) Reflex angle
Acute angle
Right angle
Obtuse angle
Straight angle
Reflex angle
Types of Angles

5. Acute angle- An angle whose measure is
more than 0 but less than 90 is called an
acute angle.
Given angle AOB measures 60 , which is less than 90 .
So, it is an acute angle.
O
O
A
B
60
Acute angle

6. All of these angles are acute:

7. Right angle-An angle whose measure is 90 is called a right angle.
Given angle POQ measures 90 .
So, it is a right angle.
O
P
O
Q
Right angle

8. Obtuse angle
– An angle whose measure is more than 90 but less than 180
is called an obtuse angle.
Given angle PQR measures 120 , which is more
than 90 but less than 180 .
So, it is an obtuse angle.
P
Q
R
120

9. °
All of these angles are obtuse:

10. Straight line angle
Straight angle – An angle whose measure is
180 called a straight angle.
Given angle BOD measures 180 .
So, it is a straight angle.
D
B O D
180

11. Reflex angle –
An angle whose measure is more than
180 but less than 360 is called a reflex angle.
Given angle PQR measures 225 .
So, it is a reflex angle.
225
225
P
Q R

12. All of these are reflex angles:

13. Summary
 Acute Angle: less than 90°
 Obtuse Angle: more than 90° but less than 180°
 Straight line Angle: at 90 °
 Reflex Angle: more than 180° but less than 360°

14. SECTION 2
Learning Objective:
To calculate unknown angles:
around a point
on a straight line
Vertically opposite angles
Parallel lines and transversal

15. Angles on a straight line -
Examples
40° a
a = ?
a = 140˚
35° b
b = ?
b = 145˚
125°
c
c = ?
c = 55˚
110°
d
d = ?
d = 70˚
e.g.1
e.g.2
e.g.3
e.g.4

16. 1) 2)

17. The angles on a straight
line add up to 180°.
a + b = 180°
The angles at a point add
up to 360°.
m + n + p = 360°
a
b
p
n
m

18. Angles around a point
Angles around a point add up to
360.
a + b + c + d = 360
a b
c
d
because there are 360 in a full turn.

19. Examples 1 & 2
a = 360° - (230° + 90°)
a = 40°
230°
a
30°
b
a = ?
b = 360° - (30° + 90°)
b = 240°
b = ?
b = 360° - (120°)
a = 360° - 320°

20. Example 3 & 4
c = ?
c = 360 – (90 + 65)
c = 360 – 155
c = 205˚
c
65˚
d = ?
d = 75˚
d = 360 – (90 + 195)
d = 360 – 285
195˚
d

21. Vertically opposite angles
When two lines intersect, two pairs of vertically
opposite angles are formed.
a
b
c
d
a = c and b = d
Vertically opposite angles are equal.

22. Vertically opposite
angles are equal.
So...
A = B
D = C

23. Examples
4)
3)

24. Parallel Lines And Transversal
Parallel Lines And Transversal
Transversal : -A transversal, or a line
that intersects two or more coplanar lines,
each at a different point, is a very useful
line in geometry. Transversals tell us a
great deal about angles.
Parallel Lines :- Parallel lines remain the
same distance apart over their entire
length. No matter how far you extend
them, they will never meet.
•Corresponding Angles
•Alternate Interior Angles
•Alternate Exterior Angles
•Interior Angles On The Same Side Of
the transversal

25. The angles that occupy the same relative position
at each intersection where a straight line crosses
two others. If the two lines are parallel, the
corresponding angles are equal
Corresponding Angles

26. Alternate Interior Angle
When two parallel lines are cut by a transversal, the two
pairs of angles on opposite sides of the transversal and
inside the parallel lines, and the angles in each pair are
congruent

27. Alternate Exterior Angle
When two parallel lines are cut by a transversal, the two
pairs of angles on opposite sides of the transversal and
outside the parallel lines, and the angles in each pair are
congruent

28. Interior Angles On The Same Side
Of the transversal
Interior angles on the same side of the transversal are
also referred to as consecutive interior angles or allied
angles or co-interior angles.
Further, many a times, we simply use the words alternate
angles for alternate interior angles.

29. Solved examples
a + 140=180
a=180-140
a=40
a=b (alternate interior angles are equal)
b=40