ANGLES

Back to: Mathematics Primary 5

HELLO, WELCOME BACK TO CLASS

 

An angle is the amount of turning or rotation of a line about a point. Angles are measured in degrees (⁰). We can use a protractor to measure an angle. The minute hand of a clock is a good example of how angles turn.

HOW TO USE THE PROTRACTOR

• Place the centre point of the protractor on the vertex of the angle.
• Line the protractor correctly by placing the 00 mark on one line of the angle.
• Read the number of degrees where the other line of the angle goes through the protractor.

TYPES OF ANGLES AND THEIR PROPERTIES

There are many kinds of angles. Each is named after its size or the amount of turning made. They include:

• Right angle
• Acute angle
• Obtuse angle
• Reflex angle

 

 

RIGHT ANGLE

This is an angle at 90⁰ (90 degrees).

 

The angle abc = 90⁰

 

ACUTE ANGLE

This is an acute which is less than 90⁰.

The angle abc is less than 90⁰.

 

OBTUSE ANGLE

This is an angle which is greater than 90⁰, but less than 180⁰.

 

 

 

REFLEX ANGLE

This is an angle which is greater than 180⁰, but less than 360⁰.

MEASURING AND CLASSIFYING ANGLES

The following properties of angles should be followed strictly when measuring angles by calculation.

1. COMPLEMENTARY ANGLES

They are two angles whose sum is equal to 90⁰. They are mostly found in a right angle triangle.

Angles XYP + QYZ = 90⁰

2. SUPPLEMENTARY ANGLES

These are two angles whose sum is equal to 180⁰. They are mostly found on a straight line. They can also be called angles on a straight line

Angles SNT + TNM = 180⁰

 

 

3. ANGLES AT A POINT

These are angles whose sum is equal to 360⁰. They are mostly used where two or more straight line crosses each other.

Angles a + b + c + d + e = 360⁰

Examples:

Find the value of the lettered angle in the figures below:

SOLUTION

These are complementary angles

54⁰ + x⁰ = 90⁰

X⁰ = 90⁰ – 54⁰ = 36⁰

The value of angle x = 36⁰

2.

Solution

These are complementary angles.

26⁰ + 2x⁰ = 90⁰

2x⁰ = 90⁰ – 26⁰

2x⁰ = 64⁰

Divide by 2

X⁰ = 64 / 2 = 32⁰

The value of angle x = 32⁰

 

3.

Solution

These are supplementary angles.

Y⁰ + 75⁰ = 180⁰

Y⁰ = 180⁰ – 75⁰= 105⁰

The value of angle y = 105⁰

Solution

These are supplementary angles.

3x⁰ + x⁰ + 2x⁰ = 180⁰

6x⁰ = 180⁰

Divide by 6

X⁰ = 180/6 = 30⁰

The value of angle x = 30⁰

 

ANGLES IN A TRIANGLE

A triangle is a closed plane figure that has three sides. Triangles have special names depending on the number of sides that are equal.

1. EQUILATERAL TRIANGLE

The three sides and angles of this triangle are equal. The angles are each 60⁰.

 

 

2. ISOSCELES TRIANGLE

Only two sides and angles of the triangle are equal.

3. SCALENE TRIANGLE

None of the three sides and angles of this triangle are equal.

4. RIGHT ANGLE TRIANGLE

One of the angles of this triangle is 90⁰.

 

 

 

CALCULATING ANGLES IN A TRIANGLE

The sum of angles in any type of triangle mentioned above is 180⁰.

Examples

Find the size of the lettered angles in the figures below:

 

Solution

This is a right angle triangle. Therefore one of the angles is 90⁰.

Sum of angles in a triangle = 180⁰

90⁰ + 54⁰ + x⁰ = 180⁰

144⁰ + x⁰ = 180⁰

X⁰ = 180⁰ – 144⁰ = 36⁰

Solution

This is a scalene triangle. None of the angles are equal.

Sum of angles in a triangle = 180⁰

105⁰ + 50⁰ + y⁰ = 180⁰

155⁰ + y⁰ = 180⁰

Y⁰ = 180⁰ – 155⁰ = 25⁰

Solution

This is an Isosceles triangle. Two of it angles are equal.

Sum of angles in a triangle = 180⁰

120⁰ + x⁰ + x⁰ = 180⁰

120⁰ + 2x⁰ = 180⁰

2x⁰ = 180⁰ – 120⁰

2x⁰ = 60⁰

Divide by 2

X⁰ = 30⁰

 

 

 

 

EXERCISES

1. Find the value of the lettered angles in the followi

 

 

 

2. Find the value of the lettered angles in the triangles below:

 

 

 

 

 

 

 

 

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