Functional Skills: Angles in 2D Shapes
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.
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
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
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
Functional Skills: Angles in 2D Shapes Example Questions
Question 1: The diagram below shows a triangle.
Find the missing angle labelled A.
[1 mark]
Angles in a triangle add up to 180\degree, so
A = 180 - 75 - 45 = 60\degree
Question 2: What is the size of each angle in an equilateral triangle?
[1 mark]
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
Question 3: The diagram below shows a parallelogram. A parallelogram has two pairs of equal angles.
Find the values of angles A, B and C.
[2 marks]
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
Functional Skills: Angles in 2D Shapes Worksheet and Example Questions
Angles in 2D Shapes L2
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