Functional Skills: Angles in 2D Shapes

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Functional Skills: Angles in 2D Shapes Revision

Angles in 2D Shapes

Here, we will look at how to find missing angles in 2D shapes, using certain rules that always apply.

There are 2 rules that you need to learn.

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Rule 1: Angles in a Triangle add up to 180\degree

If you add up each angle in a triangle, the answer will always be 180\degree.

\textcolor{red}{A + B + C = 180 \degree}

 

You can then use this rule to find the missing angles in triangles.

You may also need to use other triangle properties, such as angles in an equilateral triangle all being the same size, or two angles in an isosceles triangle being equal.

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Rule 2: Angles in a Quadrilateral add up to 360\degree

If you add up each angle in a quadrilateral, the answer will always be 360\degree.

\textcolor{blue}{A + B + C + D = 360 \degree}

 

You can then use this rule to find the missing angles in quadrilaterals.

You may also need to use other quadrilateral properties, such as lines of symmetry and equal angles.

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Example 1: Finding Missing Angles in Triangles

The diagram is an isosceles triangle. Find the missing angles in this isosceles triangle.

[2 marks]

All three angles add up to 180\degree.

So, the missing angles add up to

180 \degree - 70 \degree = 110 \degree

An isosceles triangle has two equal angles, so the missing angles are both

110 \degree \div 2 = 55 \degree

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Example 2: Finding Missing Angles in Triangles

The diagram is a right-angled triangle. Find the value of angle x.

[1 mark]

All three angles add up to 180\degree.

The triangle is a right-angled triangle, so one of the angles is 90 \degree.

So, the missing angle, x, is

 

x = 180 \degree - 90 \degree - 50 \degree = 40 \degree

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Example 3: Finding Missing Angles in Quadrilaterals

The diagram shows a quadrilateral. Find the value of angle A.

[1 mark]

All four angles add up to 360\degree.

One of the angles is 90 \degree, since it is a right-angle.

So, the missing angle, A, is

 

A = 360 \degree - 120 \degree - 90 \degree - 80 \degree = 70 \degree

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Example 4: Finding Missing Angles in Quadrilaterals

The diagram shows a quadrilateral, with two lines of symmetry. Find the values of angles A, B and C.

[2 marks]

There are two lines of symmetry, so

  • angle A = 150 \degree
  • angle B = angle C

So, the sum of angles B and C is

360\degree - 150\degree - 150\degree = 60\degree

Therefore, angle B and C are both

60\degree \div 2 = 30 \degree

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Functional Skills: Angles in 2D Shapes Example Questions

Angles in a triangle add up to 180\degree, so

 

A = 180 - 75 - 45 = 60\degree

Angles in a triangle add up to 180\degree, and each angle in an equilateral triangle is equal.

Therefore, each angle is

180 \div 3 = 60\degree

Angle A is equal to 70\degree, which is one pair of equal angles.

Therefore, the sum of angles B and C is equal to

360 - 70 - 70 = 220 \degree

So, angles B and C are both

220 \div 2 = 110 \degree

Additional Resources

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Exam Tips Cheat Sheet

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PFS

Formula Booklet

FS Level 2

Functional Skills: Angles in 2D Shapes Worksheet and Example Questions

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