Watch: Different types of triangles
Angles in triangles
All triangles have internal angles that add up to 180°, no matter the type of triangle.
- An isosceles triangle will have two angles the same size.
- In an equilateral triangle, all angles will be 60°.
- A right-angled triangle will have one angle that is 90°, which means the other two angles will have a total of 90°.
- A scalene triangle will have all angles of a different size.
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°, you have to add up the values of the angles that you do know and then subtract them from 180°:
40° + 60° = 100°
180° - 100° = 80°
Therefore:
a = 80°
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° - 50° = 130°
Angles d and e must now both equal 130°. Since we know these angles are both equal, you can find their value by halving 130°.
130° ÷ 2 = 65°
So d = 65° and e = 65°
Angles on a straight line
Angles on a straight line also add up to 180°.
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 ±«Óătv Bitesize:
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°, represented by the right angle symbol, and another is 35°. And you also know that angles on a straight line add up to 180°.
To find the unknown angle, first add the known angles together:
90° + 35° = 125°
Now subtract from 180°:
180° - 125° = 55°
The missing angle above is 55°.
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.
Quiz 2
Put your knowledge of angles in triangles to the test in this quiz.
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