Sum of Angles on a Straight line

Subject : MATHEMATICS

Class : JSS1

Term :THIRD TERM

Week : WEEK SEVEN

Reference Materials

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum

Previous Knowledge :

The pupils have previous knowledge of

Angles: Identification and properties of angles (

Behavioural Objectives :  At the end of the lesson, the pupils should be able to

• define triangles 
• list types of triangles
• calculate the values of unknown angles in triangles
• give examples of Three dimensional ( 3-D) shapes
• calculate the volume of Three dimensional ( 3-D) shapes

Content :

WEEK SEVEN

TOPIC:   ANGLE SUM OF A TRIANGLE, ANGLE ON A STRAIGHT LINE, ANGLE AT A POINT

CONTENT

(1) Angle sum of a triangle 

(2) Angles on a straight line 

(3) Angles at a point

Angle sum of a triangle

(a) Definition: A Triangle is a three-sided plane figure with three interior  angles and three sides 

(b) Types of triangles

(i) Scalene triangle 

This triangle has none of its sides or angles equal to one another . One angle may be 100 degree , other may be 50 degree and the last one may be 30 degrees 

(ii) An Isosceles Triangle: This type of triangle has two adjacent  sides equal and two angles equal.

(iii) An Equilateral Triangle

An equilateral triangle is a triangle that has all the three angles and three sides equal to each other . The sum of each interior angle of a triangle is always equal to 60 degrees

(iv) An Acute angled triangle

This type of triangle has one of its interior angles less than 90 degrees , 

a, b, c are acute angles 

(v) An Obtuse angled triangle

This type of triangle has one of its angles more than 90 degrees 

(vi) A right – angled triangle 

This triangle has one of its angles equal to 90 degrees. The side opposite the right angle is the longest side and is often called hypotenuse.

(c) Angle sum of a triangle

The sum of the three angles of a triangle is equal to 1800 proof:

To prove that the sum of angle of a triangle is equal to 1800, draw triangle ABC. Draw line LM through the top vertex of the triangle, parallel to the base BC.

Label each angle as shown in the diagram. From the above diagram 

b = d (alternate angles)

c = e (alternate angles)

But d + a + e = 1800 (sum of angles on a straight line).

:. a + b + c = d + a + e   = 1800.

Hence, the sum of angles of a triangle = 1800. 

Examples:

(i) Find the size of angle x in this triangle.

Solution

 x + 640 + 880  = 1800 (sum of angle of a triangle)

:. X + 1520  = 1800

Collect like terms:.

:. X = 1800 – 1520

:. X = 280

(ii) From the diagram below 

(a) Find the value of a 

(b) Use the value of a to find the actual values of the interior angles of the triangle.

Solution

(a) <ABC  = 2a (vertically opposite angles)

Now 2a + 3a + 5a  = 1800 (sum of angles of a triangle).

:. 10a  = 1800

:. 10a = 180 = 180

   10 10

i.e. a   = 180

(b) If a = 180

:. 2a   = 2 x 180  =  360

Again  3a  =  3 x 180   =  540

Also 5a  = 5 x 180  = 900

:. The angles are 360, 540 and 900. 

II Angles on a straight line

Definition: When a straight line stands on another straight line two adjacent angles are formed. The sum of the two adjacent angles is 1800.

:. AOC + BOC  = 1800

Examples

(i) In this figure, find b.

Solution

700 +b + 600 = 1800 (supplementary angles)

:. B + 1300  = 1800

Collect like terms

:. B = 1800 – 1300

:. B = 500

(2) In the diagram, find the value of x. 

SOLUTION

Since 600 + x + 450 + 420  = 1800 (sum of angles on a straight line)

:. X + 600 + 450 + 420  = 1800

:. X + 1470  = 1800

Collect like terms

:. X = 1800 – 1470

:. X = 330

EVALUATION QUESTION

Calculate the labelled angle in this diagram. 

(iii) Angles at a point

(a) Example: When a number of lines meet at appoint they will form the same number of angles. The sum of the angles at a point is 3600

AOB + BOC + COD + DOA  = 3600

(b) Examples:

(1) Find the value of each angle in the figure.

Solution

Since x + 2x + 5x + 1200 = 3600 (angles at a point)

8x + 1200 = 3600

Collect  like terms

8x = 3600 – 1200

 8x = 2400

 8x   =  2400

    8           8

:. X = 300

Hence 2x = 2 x 300 = 600

Also 5x = 5 x 300  = 1500

From the diagram find the value of X 

Solution

Since 3200 + x + x = 3600 (angle at a point) 

3200 + 2x = 360

Collect like terms 

 2x = 3600 – 3200 

2x = 400

X = 400 = 200

2

:. X =200

Presentation

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

Evaluation:

EVALUATION QUESTION

1. In a triangle, one of the angles is three times the other. If the third angle is 480, find the sizes of the other two angles.
2. Find the value of k in the diagram below 

GENERAL EVALUATION QUESTION 

1. Find the angles marked with letters in this figure

From the diagram, find the angle marked with alphabet 

WEEKEND ASSIGNMENT 

Objective

1. In this diagram angles x and y are called. 

(a) Complementary angles (b) Supplementary angles (c) Conjugate angles (d) vertically opposite angles (e) alternate segment angles 

(2) The sum of adjacent angles on a straight lines is __________ (a) 3600 (b) 900 (c) 3 right angles (d) 1500 (e) 2 right angles 

(3) Find the value of a in the diagram below 

(a) 640 (b) 160 (c) 320 (d) 450 (e) 500

(4) Find the value of a in the diagram below 

(a) 1000 (b) 400 (c) 800 (d) 500 (e) 300

(5) The value of angle z in the diagram below is 

(a) 720 (b) 700 (c) 1500 (d) 1200 (e) 1100

Theory 

1. Find the value of x and hence find the size of each angle 

2. State the sizes of the lettered angles in the figure below, give reasons 

Conclusion :

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where  the needs arise.

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