By studying this lesson, you will be able to,
● identify an angle,
● identify a right angle and
● identify an acute angle, an obtuse angle, a straight angle and a reflex angle, in terms of the right angle.
7.1 Identifying an angle
The following figure depicts a part of a line drawn straight. This is known as the straight line segment AB.
An angle is formed by two straight line segments meeting as shown in the figure. The point at which the two straight line segments meet is known as the vertex of the angle.
The two straight line segments are known as the arms of the angle. The angle is marked with a curved line segment as indicated in red.
Several angles are shown in the following figure.
We see angles such as those given above in various places in the environment. The following figures are several such examples.
The knowledge of angles is used in many practical situations such as in the construction of roofs and the production of household items
Exercise 7.1
(1) From the following figures, select the ones which depict angles and write down the corresponding letters.
(2) From each pair of angles in the figures given below, select the larger one and write the corresponding letter.
7.2 The right angle
The final figure illustrates how the lamina has been divided into four equal parts by the two straight line segments.
● Here, four angles of equal size have been created as depicted in the figure.
● An angle of magnitude equal to the magnitude of each of these angles is known as a right angle.
A figure showing the positions of the minute hand and the hour hand when it is 3 o’clock and two figures of several angles drawn on square ruled papers are given on page 88. All the angles in the above figures are right angles which are equal in magnitude.
The symbol in red in the figure is used to denote a right angle.
Several places in the class room, where the shape of a right angle can be observed are given below.
● The position at which two edges of the cover of a book meet.
● A corner of the surface of the teacher’s table.
● A corner of the black board.
Exercise 7.2
(1) From the following angles, select the ones which are right angles and write down their numbers.
(2) Draw a right angle on a square ruled paper. Use the relevant symbol to denote the fact that it is a right angle.
(3) Write down 5 situations in the environment, where the shape of a right angle can be observed.
7.3 Identifying different types of angles in terms of the right angle
1. Acute Angles Angles which are smaller in magnitude than a right angle are known as acute angles.
2. Straight Angles Angles which are equal in magnitude to two right angles are known as straight angles.
3. Obtuse Angles Angles which are larger in magnitude than a right angle but smaller in magnitude than a straight angle are known as obtuse angles.
4. Reflex Angles Angles which are larger in magnitude than a straight angle but smaller in magnitude than four right angles are known as reflex angles.
Now, you have identified five types of angles as right angles, acute angles, straight angles, obtuse angles and reflex angles.
Exercise 7.3
(1) Write down which type the angle marked between the hour hand and the minute hand of each clock face belongs to.
(2) Write down in order, the type of each angle denoted by the numbers from 1 upto 10 in the following figures.
(3) For each of the following figures, write down the type of angle that is denoted by each number together with the relevant number.
(4) Copy the following table in your exercise book and complete it by writing the type of angle denoted by 1 and 2 in each of the figures given below.
(5) On a square ruled paper, draw two angles of each type that is mentioned below. Mark each of the angles.
• Acute angle
• Right angle
• Obtuse angle
• Straight angle
• Reflex angle
(6) When window grills are made, the iron rods are welded together such that they form various types of angles. Illustrate such situations in your environment to indicate various types of angles.
