# Lesson Notes By Weeks and Term - Junior Secondary School 1

ANGLE SUM OF A TRIANGLE, ANGLE ON A STRAIGHT LINE, ANGLE AT APOINT

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 3rd TERM

REFERENCE TEXTBOOKS

• New General Mathematics, Junior Secondary School Book 1
• Essential Mathematics for Junior Secondary School Book 1

WEEK SEVEN

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

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 angles.

(b)    Types of triangles

(i)    Scalene triangle

This triangle has no sides and no angles square.

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

(iii)    An Equilateral Triangle

This type of triangle has all its sides equal and all its angles equal each     angle is 600.

(iv)    An Acute angled triangle

This type of triangle has each of its angle less than 900 i.e. each angles is     acute.

a, b, c are acute angles

(v)    An Obtuse angled triangle

This type of triangle has one of its angles more than 900

(vi) A right – angled triangle

This triangle has one of its angles equal to 900. 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)

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.

(1)    New general mathematics for JSS 1 by JB Channon and others pages 136 - 138

(2)    Essential mathematics for JSS 1 by AJS Oluwasanmi

(3)    MAN mathematics book 1 pages 199.

(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 - 320

2x = 400

X = 400 = 200

2

:. X =200

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

1. Essential Mathematics for JSS 1 by A.J.S. Oluwasanmi Pages 202 – 207
2. New general mathematics for JSS 1 by J.B. Channon and other pages 135 – 144

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

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