CORRESPONDING ANGLES, ALTERNATE AND VERTICALLY OPPOSITE ANGLES

**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

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WEEK 6

**TOPIC: CORRESPONDING ANGLES, ALTERNATE AND VERTICALLY OPPOSITE ANGLES**

**CONTENT**

(I)��� Corresponding angles

(II)��� Alternate angles�

(III)��� Vertically opposite angles�

(i)��� Corresponding angles�

(a)��� Definition�

(1)��� Adjacent angles�

When two angles lie beside each other and have a common vertex, we say they are adjacent to each other.

From above diagram, AOB is adjacent to BOC. BOC is adjacent to AOB.

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

Since angles XOZ and YOZ lie next to each other, we say they are adjacent angles. Since the sum of angles on a straight line is 1800 XOZ + YOZ = 1800i.e a + b = 1800. The sum of adjacent angles on a straight line is 1800.

(2)��� Complementary angles�

If two angles add up to 900, they are said to be complementary.�

Since x + B = 900 :- x and B are complementary angles. Therefore, complementary angles add up to 900.

(3)��� **Supplementary angles**

**��� **If the sum of two angles add up to 1800, they are said to be supplementary.

x + y + z = 1800 Note x, y, z are supplimentary angles. Therefore, supplimentary angles add up to 1800. Note also that adjacent angles on a straight line are said to be supplimentary.

(4)��� **Angles at a point**

The sum of the angles at a point is 3600

a + b + c + d = 3600

Therefore, angles at a point add up to 3600

(ii)��� conjugate angles add up to 3600 we say that they are conjugate angles

x + y = 3600, therefore x and y are called conjugate angles

(5)��� **Transversal**

A line cutting a pair of lines (whether parallel or not is called a transversal.

(b)��� **Corresponding angles**

When a transversal cut parallel lines corresponding angles formed are equal.

Corresponding angles are sometimes called F angles. You can easily recognise corresponding angles by looking for F angles as shown in the diagrams below.

a = b

Angles a and b are called corresponding angles.

(ii)��� **Co-interior angles**

Co-interior angles are supplimentary angles because they add up to 1800

In the diagram above:- x + y = 1800 (complimentary angles). Similarly a + b = 1800 Note that the shape of the diagrams look like letter C and U, hence co-interior angles are sometimes called C or U angles

Example

Calculate angles a and b shown in this diagram

A = 1260 (corresponding angles)

B = 540 (corresponding angles)

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In this diagram, find the sizes of the lettered angles, give reasons.

When a transversal cut parallel lines alternate angles formed are equal.

a = b��� ��� ;��� ��� x = y

Angles a and b are called alternate angles also angles x and y are called alternate angles. You can quickly recognize alternate angles by looking for angles formed by letter Z as shown in the diagram below.

In the above figures m = n, p = q.

Note, alternate angles are sometimes called Z angles.

Fined the values of a and b in the diagram

**Solution**

2a + 1 = 1110 (alternate angles)

collect like terms�

2a� =� 1110 - 10

:. 2a� =� 1100

:. 2a� =� 1100

����2� � � � � 2

1.e. a = 550

Also b = 700 (alternate angles)

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**III VERTICALLY OPPOSITE ANGLES**

When two straight lines intersect as shown in the figure below, then the vertically opposite angles are equal. They are also called X angles.�

A = b (vertically opposite angles)

X = y (vertically opposite angles)

Therefore, vertically opposite angles are equal.

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Example

Find� � � � and�

Solution

X = 1200 (vertically opposite angles)

B = 600 (vertically opposite angles)

**EVALUATION QUESTION**

Find angles x, y and z in the above diagram

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**GENERAL EVALUATION QUESTION**

- Find the size of the following angles marked with letters�

- Find angles p, q and r in the diagram below

- New General Mathematics for JSS I by JB Channon and others. Pages 139 - 141
- Essential Mathematics for JSS I by AJS Oluwasanmi. Pages 205 - 208
- STAN Mathematics for JSS I Page 191.

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**WEEKEND ASSIGNMENT**

**OBJECTIVE**

(1)���

(2)��� Find the value of x in the diagram below

(a) 1350 (b) 1800 (c) 350 (d) 450 (e) 3600

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(3)��� In the diagram below find the value of x�

(a) 380 (b) 750 (c) 800 (d) 1130 (e) 670

(4)��� X0Y and Y0Z are adjacent on a straight line X0Z. If X0Y = 580 then Y0Z is _________ (a) 320 (b) 1220 (c) 1320 (d) 2380 (e) 3020

(5)��� Complete the following sentence correctly. Vertically opposite angles (a) are alternate (b) add up to 1800 (c) are corresponding (d) are equal (e) add up to 3600

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**THEORY**

(1)��� Find the angles marked with letters in the following diagrams

(a)

(b)

(2)��� In the diagram below find a,b,c,d,e.

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