Angles

Angles

Angles are measured using degrees (°).

Your child will need to know the different types of angles, and may also be asked to work out a missing angle on a diagram using angle rules.

Types of Angle

There are three types of angle your child needs to know:

  • An acute angle measures between \bf{0°} and \bf{90°}
  • A right-angle measures exactly \bf{90°}, and is shown by a square symbol on a diagram.
  • An obtuse angle measures between \bf{90°} and \bf{180°}

Angle Rule \bf{1}

Angles around a point add up to \bf{360°}

 

Example: Find the value of angle x in the diagram.

All the angles around a central point must add up to 360°

The angles we are given so far add up to 100+45+75=220°

So angle x must be 360-220=140°

Angle Rule \bf{2}

Angles on a straight line add up to \bf{180°}

 

Example: Find the value of angle a in the diagram.

All the angles on a straight line must add up to 180°

The angle we are given is 150°

So angle a must be 180-150=30°

Angle Rule \bf{3}

Angles in a triangle add up to \bf{180°}

 

Example: Find the value of angle p in the diagram.

All three angles in the triangle must add up to 180°

The angles we are given so far add up to 25+80=105°

So angle p must be 180-105=75°

Angle Rule \bf{4}

Angles in a quadrilateral add up to \bf{360°}

 

Example: Find the value of angle f in the diagram.

All four angles in the quadrilateral must add up to 360°

The angles we are given so far add up to 125+80+52=257°

So angle f must be 360-257=103°

Example: Finding Missing Angles in a Composite Shape

A composite shape is made up of smaller shapes. Your child may have to use more than one rule to find a missing angle in a composite shape.

Example: Find the values of:

a) Angle a

b) Angle b

c) Angle c

a) The left hand shape is a quadrilateral, and we know the angles in a quadrilateral add up to 360°

The angle with the square symbol must be a right-angle, which is 90°

So we know three angles in the quadrilateral. They add up to 90+68+80=238°

So angle a must be  360-238=122°

 

b) We know angles on a straight line add up to 180°

We also know that angle a=122°

So angle b must be 180-122=58°

 

c) The right hand shape is a triangle, and we know the angles in a triangle add up to 180°

We also know that angle b=58°

So we know two angles in the triangle. They add up to 72+58=130°

So angle c must be 180-130=50°

Angles Example Questions

Question 1: Which angle on the shape below is acute?

[1 mark]

An acute angle is bigger than 0° but smaller than 90°, so must be angle D.

  Question 2: Find the value of angle x on the diagram.

 [1 mark]

Angles on a straight line add up to 180°, so x=180-55=125°

Question 3: Find the value of angle k on the diagram.

[1 mark]

Angles in a triangle add up to 180°

The two angles we know add up to 50+85=135°

So k=180-135=45°

Question 4: What is the size of the angle marked x between the hands on this clock?

[3 marks]

The angle around the centre point of the clock is 360°

We know there are 12 hours equally spaces around the clock, so the angle between each hour must be 360\div12=30°

The hands are 4 hours apart.

So the angle between them must be 4\times30°=120°

Question 5: Find the values of:

a) angle a

b) angle b

c) angle c

d) angle d

[4 marks]

a) The angle with a square symbol is a right-angle, which is 90°

So a=90-60=30°

 

b) The right hand shape is a quadrilateral, and we know the angles in a quadrilateral add up to 360°.

We know three of the angles in the quadrilateral, which add up to 30+110+95=235°.

So b=360-235=125°

 

c) We know angles on a straight line add up to 180°, so c=180-125=55°

 

d) The left hand shape is a triangle, and we know the angles in a triangle add up to 180°

We know two of the angles in the triangle, which add up to 60+55=115°

So d=180-115=65°