Modul Lines and Angle 1

LINES AND ANGLE 1

LINES AND ANGLE 1

MEASURING ANGLES USING A PROTRACTOR

PROTRACTORe.g: Measure the angle in diagram below.

The steps to measure an unknown angle :

Place the centre of the protractor on vertex B

Adjust the base line so that it is aligned with the line BC

Read the value of from the inner scale

Solution :

EXERCISEMeasure all of angles in diagram below.

1.

2.

3.

4.

DRAWING ANGLES USING A PROTRACTOR

E.g:

a. How to draw an angle ABC which measures ?

Draw a straight horizontal straight line BC. Mark point B as the vertex

Place the centre of the protractor at vertex B and adjust the base line so that it is aligned with the line BC

Find the angle on the protractor scale and mark point A

Remove the protractor and draw a straight line from point B to point A

Label

b. Draw a reflex angle

Solution:

EXERCISE

Use a protractors to draw each of all angles below :

1.

2.

3.

4.

5.

6.

7.

8.

THE SUM OF ANGLEa. The sum of angles on a straight line is

b. The sum of angles at a point line is

E.g :

1. Calculate in the following diagram.

2. Find the value of x

EXERCISE

1. Calculate the value of p in each of the following figures

a.

Solution:

b.

Solution :

c.

Solution:

d.

Solution:

2. Determine the value of q in each of the following figures

a.

Solution:

b.

Solution :

c.

Solution:

d.

Solution:

PARALLEL LINE

PERPENDICULAR LINES

EXERCISE1. Determine if the pairs of straight lines below are parallel

a.

Solution :

b.

Solution:

2. Using a protractor, determine whether the line PQ is perpendicular to RS or not.a.

Solution :

b.

Solution:

INTERSECTING LINES

a. Vertically opposite angle

a and c are vertically opposite anglesb and d are vertically opposite angles

therefore, a = c and b = d

c. Supplementary angles

b. Complementary angles

d. Adjacent angles

EXERCISESolve all of questions below.

a. In the following diagram, lines PQ and

RS intersect at O. Determine the value of

P

Solution:

b. In the following diagram, find the value

of x

Solution:

c. p and q are complementary angles. Given that p = 550 , find the value of q.

Solution:

d. In the following figure, find the value of

p.

Solution:

LINES AND ANGLES

Lines

Angles

A

C

B

P

EMBED Equation.3

R

Q

EMBED Equation.3

D

F

E

U

EMBED Equation.3

T

S

L

EMBED Equation.3

M

N

B

EMBED Equation.3

EMBED Equation.3

Solution:

The sum of the given angles

= EMBED Equation.3

= EMBED Equation.3

Subtract this sum from EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

Solution:

x EMBED Equation.3

EMBED Equation.3

Two parallel lines are parallel if

They never meet or intersect

The perpendicular distance between two lines is the same at all points on either line

PQ is parallel to RS ( PQ // RS)

AB is parallel to CD ( AB // CD )

** // --- symbol for parallel

Two straight lines are perpendicular to each other if they intersect at a right angle (900 )

PQ is perpendicular to RS and vice versa

Two straight lines intersect if they meet only at one point

Line PQ intersect line RS at point T

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