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Basic angle rules

Basic angle rules

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Explainer Video

Tutor: Dylan

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\degree180°.


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\degree180°. 

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


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



Angles on a straight line

Angles on a straight line add up to 180°180\degree180°.


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\degree180°. 

180°−100°=80°180\degree - 100\degree = 80\degree180°−100°=80°

​​

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

 


Angles in a quadrilateral

Angles in a quadrilateral add up to 360°360\degree360°.


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\degree360°. Subtract the sum of the known angles from 360°360\degree360°. 

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}80°+120°+40°360°−240°​=240°=120°​


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



Angles around a point

Angles around a point add up to 360°360\degree360°.


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\degree360°, so take 140°140\degree140° away from 360°360\degree360°.

360°−140°=220°360\degree- 140\degree= 220\degree360°−140°=220°​​


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

 


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 ACACAC and BCBCBC​. If ∠BAC\angle BAC∠BAC​ is 50°50\degree50°, find the size of ∠ACB\angle ACB∠ACB​.


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


∠BAC\angle BAC∠BAC​ and ∠ABC\angle ABC∠ABC​ are both 50°50\degree50°, as they are the base angles of the triangle. As angles in a triangle add up to 180°180\degree180°, you can find ∠ACB\angle ACB∠ACB​ by subtracting the sum of ∠ABC\angle ABC∠ABC​ and ∠BAC\angle BAC∠BAC​ from 180°180\degree180°​.

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


∠ ACB =80°‾\underline{\angle\ ACB\ = 80\degree}∠ ACB =80°​

​

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Angles around a point and on a straight line

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Angles around a point and on a straight line

Angle rules

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Angle rules

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Basic angle rules

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Basic angle rules

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FAQs - Frequently Asked Questions

What do angles on a straight line add up to?

Angles on a straight line add up to 180 degrees.

What do the angles in a triangle add up to?

The angles in a triangle add up to 180 degrees.

What is an isosceles triangle?

An isosceles triangle is a triangle with two sides equal in length and two equal angles.

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