Basic angle rules

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Summary

Basic angle rules

​​In a nutshell

There are five rules involving angles on lines and shapes. These rules refer to angles in a triangle, angles on a straight line, angles in a quadrilateral, angles around a point and angles in an isosceles triangle. The rules help to find missing angles on lines and in shapes.



Angles in a triangle

The angles in a triangle add up to 180°180\degree.


Example 1

Find the size of the missing angle in the triangle:


Maths; Angles and geometry; KS4 Year 10; Basic angle rules


Angles in a triangle add up to 180°180\degree

70°+30°=100°180°100°=80°\begin{aligned}70\degree+30\degree & =100\degree \\180\degree-100\degree &=80\degree\end{aligned}​   


The missing angle is 80°\underline{80\degree}.



Angles on a straight line

Angles on a straight line add up to 180°180\degree.


Example 2

Find the size of the missing angle on the straight line:


Maths; Angles and geometry; KS4 Year 10; Basic angle rules


Angles on a straight line add up to 180°180\degree

180°100°=80°180\degree - 100\degree = 80\degree

​​

The missing angle is 80°\underline{80\degree}.

 


Angles in a quadrilateral

Angles in a quadrilateral add up to 360°360\degree.


Example 3

Find the size of the missing angle in the quadrilateral shown:


Maths; Angles and geometry; KS4 Year 10; Basic angle rules


Angles in a quadrilateral add up to 360°360\degree. Subtract the sum of the known angles from 360°360\degree

80°+120°+40°=240°360°240°=120°\begin{aligned}80\degree+120\degree+40\degree &= 240\degree \\ 360\degree- 240\degree &= 120\degree\end{aligned}


The missing angle is 120°\underline{120\degree}.



Angles around a point

Angles around a point add up to 360°360\degree.


Example 4

Find the size of the missing angle:


Maths; Angles and geometry; KS4 Year 10; Basic angle rules


Angles around a point add up to 360°360\degree, so take 140°140\degree away from 360°360\degree.

360°140°=220°360\degree- 140\degree= 220\degree​​


The missing angle is 220°\underline{220\degree}.

 


Angles in an isosceles triangle

Isosceles triangles have two sides equal in length and two equal angles. The two equal angles are sometimes referred to as the 'base angles' in an isosceles triangle. If you know one of the angles in an isosceles triangle, the other two angles can be found easily.


Example 5

The isosceles triangle has equal sides ACAC and BCBC​. If BAC\angle BAC​ is 50°50\degree, find the size of ACB\angle ACB​.


Maths; Angles and geometry; KS4 Year 10; Basic angle rules


BAC\angle BAC​ and ABC\angle ABC​ are both 50°50\degree, as they are the base angles of the triangle. As angles in a triangle add up to 180°180\degree, you can find ACB\angle ACB​ by subtracting the sum of ABC\angle ABC​ and BAC\angle BAC​ from 180°180\degree​.

50°+50°=100°180°100°=80°\begin{aligned}50\degree+50\degree &= 100\degree \\180\degree - 100\degree &= 80\degree\end{aligned}​​


 ACB =80°\underline{\angle\ ACB\ = 80\degree}


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FAQs - Frequently Asked Questions

What do angles on a straight line add up to?

What do the angles in a triangle add up to?

What is an isosceles triangle?

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