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Level 3-4 Shapes - Angles
This triangle used in the game of pool is an equilateral triangle.

Level 3-4 Shapes - Angles

Angles are all around us. Learn to name, measure, and calculate angles, including straight lines, triangles, and at a point, using a protractor and angle facts.

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Fascinating Fact:

When you look up at a tall building, the angle between your line of sight and the ground is called the angle of elevation.

In KS3 Maths, you will classify, measure, and calculate angles. Use a protractor to read degrees, apply angle sums on straight lines and in triangles, and use facts around a point to find missing angles.

  • Acute angle: An angle less than 90°.
  • Obtuse angle: An angle between 90° and 180°.
  • Reflex angle: An angle between 180° and 360°.
What are the main types of angles in KS3?

Acute is less than 90°, right angle is 90°, obtuse is between 90° and 180°, straight is 180°, reflex is between 180° and 360°, and a full turn is 360°.

How do you measure an angle with a protractor?

Place the protractor’s centre on the vertex and align the baseline with one arm. Start at 0 on the correct scale, then read the mark where the other arm crosses.

What angle facts help find missing angles?

Angles on a straight line add to 180°. Angles around a point add to 360°. Angles in a triangle add to 180°. Use these to calculate unknowns.

1 .
An angle that is 90o is a(n) .......
acute angle
obtuse angle
reflex angle
right angle
These are found in squares and other rectangles
2 .
An angle that is between 90o and 180o is a(n) .......
acute angle
obtuse angle
reflex angle
right angle
Think of obtuse angles as 'blunt' and acute angles as 'sharp'
3 .
The three interior angles in a triangle add up to what?
90o
180o
270o
360o
An equilateral triangle has 3 interior angles each measuring 60 degrees each (3 x 60 = 180)
4 .
A circle is divided into a number of parts or degrees. How many are there?
90o
180o
270o
360o
The four interior angles of a quadrilateral also add up to 360o
5 .
Two interior angles in a triangle are 35o and 55o. What is the 3rd angle?
75o
85o
90o
95o
Take 35 and 55 from 180 to find the answer
6 .
Each internal angle of a regular pentagon is 108o. What is the total number of internal degrees?
180o
360o
540o
720o
Pentagons have 5 internal angles so just multiply 108o x 5
7 .
The internal angles of a regular hexagon add up to 720o. How many degrees is each one?
60o
90o
120o
150o
There are six internal angles in a hexagon. A regular hexagon has six equal angles
8 .
An angle that is between 180o and 360o is a(n) .......
acute angle
obtuse angle
reflex angle
right angle
Every internal angle has a corresponding reflex angle. Together they add up to 360o
9 .
Angles on a straight line add up to what?
90o
180o
270o
360o
A straight line is half a circle
10 .
An angle that is between 0o and 90o is a(n) .......
acute angle
obtuse angle
reflex angle
right angle
Think of obtuse angles as 'blunt' and acute angles as 'sharp'
You can find more about this topic by visiting BBC Bitesize - Angles

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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