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 0°bf{0°} and 90°bf{90°}
  • A right-angle measures exactly 90°bf{90°}, and is shown by a square symbol on a diagram.
  • An obtuse angle measures between 90°bf{90°} and 180°bf{180°}
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Angle Rule 1bf{1}

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

 

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

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

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

So angle xx must be 360−220=140°360-220=140°

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Angle Rule 2bf{2}

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

 

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

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

The angle we are given is 150°150°

So angle aa must be 180−150=30°180-150=30°

Angle Rule 3bf{3}

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

 

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

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

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

So angle pp must be 180−105=75°180-105=75°

Angle Rule 4bf{4}

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

 

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

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

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

So angle ff must be 360−257=103°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 aa

b) Angle bb

c) Angle cc

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

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

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

So angle aa must be  360−238=122°360-238=122°

 

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

We also know that angle a=122°a=122°

So angle bb must be 180−122=58°180-122=58°

 

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

We also know that angle b=58°b=58°

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

So angle cc must be 180−130=50°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°0° but smaller than 90°90°, so must be angle DD.

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

 [1 mark]

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

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

[1 mark]

Angles in a triangle add up to 180°180°

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

So k=180−135=45°k=180-135=45°

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

[3 marks]

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

We know there are 1212 hours equally spaces around the clock, so the angle between each hour must be 360÷12=30°360div12=30°

The hands are 44 hours apart.

So the angle between them must be 4×30°=120°4times30°=120°

Question 5: Find the values of:

a) angle aa

b) angle bb

c) angle cc

d) angle dd

[4 marks]

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

So a=90−60=30°a=90-60=30°

 

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

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

So b=360−235=125°b=360-235=125°

 

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

 

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

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

So d=180−115=65°d=180-115=65°