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Watch: Different types of triangles

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Angles in triangles

All triangles have internal angles that add up to 180掳, no matter the type of triangle.

Isosceles, equilateral, right-angled and scalene triangles
  • An isosceles triangle will have two angles the same size.
  • In an equilateral triangle, all angles will be 60掳.
  • A right-angled triangle will have one angle that is 90掳, which means the other two angles will have a total of 90掳.
  • A scalene triangle will have all angles of a different size.
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Example 1

Look at this scalene triangle. How would you work out the value of a?

Since you know that all angles in a triangle add up to 180掳, you have to add up the values of the angles that you do know and then subtract them from 180掳:

40掳 + 60掳 = 100掳

180掳 - 100掳 = 80掳

Therefore:

a = 80掳

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Example 2

How would you find two missing angles on an isosceles triangle?

Use your knowledge about isosceles triangles - two angles are always the same size.

Find out what the total missing value is first:

180掳 - 50掳 = 130掳

Angles d and e must now both equal 130掳. Since we know these angles are both equal, you can find their value by halving 130掳.

130掳 梅 2 = 65掳

So d = 65掳 and e = 65掳

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Angles on a straight line

Angles on a straight line also add up to 180掳.

If a straight line has been split into three separate angles, it looks as if three corners of a triangle have been put together - just like in this video from 91热爆 Bitesize:

A short video on how to show the angles in a triangle add up to 180掳.

So if you had a missing angle on a straight line, you would apply the same logic as finding the missing angle in a triangle.

You know that one of the angles is 90掳, represented by the right angle symbol, and another is 35掳. And you also know that angles on a straight line add up to 180掳.

To find the unknown angle, first add the known angles together:

90掳 + 35掳 = 125掳

Now subtract from 180掳:

180掳 - 125掳 = 55掳

The missing angle above is 55掳.

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Activities

Quiz 1

Use what you know about angles in triangles to find the missing angles in this quiz.

The triangles are not drawn to scale so you can't use a protractor.

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Quiz 2

Put your knowledge of angles in triangles to the test in this quiz.

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More on Lines and angles

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