**CONTENT**

DEFINITION OF ANGLES

TYPES OF ANGLES

BISECTION AND CONSTRUCTION OF ANGLES.

## ANGLES

An angle is formed when two straight lines intersect or meet at a point.

The sum of angle at the centre of a complete circle is 360^{0.}

**TYPES OF ANGLES**

- Acute angles: – These are angles that are less than 90
^{0}. - Right angle: – This is an angle that is equal to 90
^{0}. - Obtuse angles: – These are angles that are greater than 90
^{0}but less than 180^{0}. - Reflex angles: – These are angles that are greater than 180
^{0}but less than 360^{0}. - Complementary angles: – These are angles that sum up to 90
^{0}. - Supplementary angles: – These are angles that sum up to 180
^{0}.

**EVALUATION**

- Define an angle.
- Mention five types of angle and describe them.

**CONSTRUCTION OF ANGLES**

The following are several ways of constructing or drawing angles:

- Using a setsquare
- Using a combination of setsquares
- Using a protractor
- Using a pair of compasses

**HOW TO CONSTRUCT ANGLES USING SETSQUARE**

Standard angles are angles 30^{0},45^{0}, 60^{0} and 90^{0}. These angles can be drawn by simply using a setsquare. The method is simply choosing the appropriate setsquare that has the angle that is to be drawn. Thus 30^{0}-60^{0} setsquare is used to draw 30^{0}, 60^{0} and 90^{0}. Similarly, the 45-45 setsquare is used to draw 45^{0} and 90^{0}.

**EVALUATION**

With the aid of a set square construct the following angle: i)90^{0} ii) 60^{0} iii)45^{0}

**COMBINATION OF SETSQUARES**

Setsquares can be combined to construct the following angles:

- To construct 75
^{0}, combine 45^{0}and 60^{0}setsquares

** 180**^{0}**– (60**^{0}** + 45**^{0}**)= 75**^{0}

- To construct 135
^{0}, combine 45^{0}and 90^{0}

** 45**^{0}**+ 90**^{0}** = 135**^{0}

- To construct 105
^{0}, combine 60^{0}and 45^{0}

** 45**^{0}**+ 60**^{0}** = 135**^{0}

**EVALUATION**

- Combine the sets-square to construct angles75
^{0}and 135^{0}. - Construct angle 60
^{o}

**HOW TO DRAW AN ANGLE USING A PROTRACTOR**

Procedure

- Place the protractor on the line from which the angle is to be formed. The baseline marked O at one end and, 180 marked at the other end.
- Set the centre of the protractor to start from where the vertex of the angle will be.
- Mark the required degree of the angles to be drawn.
- Use a straight line to join the marked point at the angle to the point vertex of the angle

**EVALUATION**

- Measure the following angles using your protractor

a) 88^{0} b)170^{0} c)275^{0} d) 300^{0} e)15^{0}

- Construct angle 30
^{o}

**How to construct Angles Using a Pair of Compasses **

**60 ^{0}**

Procedure

- Draw a straight line and mark the centre O.
- From O, using a convenient radius at point A draw an arc (almost a quadrant).
- With same radius draw another arc to intersect the first arc at C.
- Draw a line from O through the point of intersection.

The angle formed is 60^{0}

**90 ^{0}**

Procedure

- Draw a straight line and mark the centre O.
- From O draw a semicircle to touch the straight line at A and B.

- From A, with longer radius, draw an arc at the centre up.

- From B, with longer radius, draw an arc at the centre up to intersect at C.

- Draw a line from O through C.

The angle COA and COB is 90^{0}

**BISECTION OF ANGLES**

**To bisect a given angle**

- Draw a given angle ABC.
- With centre B and any convenient radius draw an arc to cut AB to D and BC at E.
- With centre A
^{1 }and any small radius an arc. - With centre E and the same radius draw an arc to intersect the previous one at F.
- Join BD, BD bisects angle ABC, i.e. angle ABD= DBC.
- Use a protractor to check angles ABF and CBF.

The following angles can be constructed by bisection:

- 30
can be constructed by bisecting 60^{0}^{0} - 15
can be constructed by bisecting 30^{0}^{0} - 12.5
can be constructed by bisecting 15^{0}^{0} - 45
can be constructed by bisecting 90^{0}^{0} - 22.5
can be constructed by bisecting 45^{0}^{0}

**READING ASSIGNMENT**

‘Read about TRIANGLES’

- MELROSE, Basic Science and Technology, Book 2 page 77-79
- NERDC-BASIC TECHNOLOGY, BOOK 2, page 46- 51

WEEKEND ASSIGNMENT

- The angle that FC makes when constructed perpendicular with line AB is _______ (a) 180
^{0}(b) 270^{0}(c) 90^{0}(d) 120^{0} - The line FC is called __________ (a) vertical (b) perpendicular (c) Horizontal (d) incline
- Which of the following drawing materials cannot be used to construct a straight line? (a) Compass (b) protractor (c) Ruler (d) pencils
- Angles that sum up to 180
^{0 }is called __________ (a) supplementary (b) complementary (c) Reflex (d) obtuse - The line for all visible outlines is called ____________ (a) Thin continuous line (b) Thick continuous line (c) short dashes (d) Zig – Zag lines.

THEORY

- With the aid of a protractor measure the following angles

(a)15^{0} (b)70^{0} (c)150^{0} (d)220^{0} (e)300^{0}. With the aid of compasses and a ruler construct angle 60^{0} and 30^{0}

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