Angle rules

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Proportion


Ratio


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Tutor: Labib

Summary

Angle rules

In a nutshell

There are four rules you have to know about angles. You can apply these rules to solve problems involving missing angles.



The four angle rules

Here are the four rules you need to know.


​​RULE

DIAGRAM

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

Maths; Lines and angles; KS3 Year 7; Angle rules

α+β+γ=180°\alpha+\beta+\gamma=180\degree​​

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

Maths; Lines and angles; KS3 Year 7; Angle rules

A+B=180°A+B=180\degree​​

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

Maths; Lines and angles; KS3 Year 7; Angle rules


α+β+γ+δ=360°\alpha+\beta+\gamma+\delta=360\degree​​

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


Maths; Lines and angles; KS3 Year 7; Angle rules

α+β+γ+δ=360°\alpha+\beta+\gamma+\delta=360\degree​​


Note: A quadrilateral is another name for a shape with 4 sides.



Missing angle problems

To solve problems involving missing angles, look at the question and see which rule applies to it. You may have to label unknown angles with xx​ and use algebra to solve for them.


Example

In the triangle below, the value of β\beta is 60°60\degree. The angle γ\gamma is 20°20\degree more than the angle α\alpha. What is the size of the angle α\alpha?


Maths; Lines and angles; KS3 Year 7; Angle rules


This question concerns angles in a triangle, so use the fact that the angles in a triangle add up to 180°180\degree.

α+β+γ=180\alpha+\beta+\gamma=180​​

α+60+γ=180\alpha+60+\gamma=180​​

α+γ=120\alpha+\gamma=120​​


The question also says that the angle γ\gamma is 20°20\degree more than the angle α\alpha. Algebraically, this means that:

γ=20+α\gamma=20+\alpha​​


Use this new information together with the first equation to solve for α\alpha:

α+γ=120\alpha+\gamma=120​​

α+(20+α)=120\alpha+(20+\alpha)=120​​

2α+20=1202\alpha+20=120​​

2α=1002\alpha=100​​

α=50\alpha=50​​


The size of the angle α\alpha  is 50°\underline{50\degree}.


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Exercises

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FAQs - Frequently Asked Questions

How do you solve problems involving missing angles?

What are the rules for angles in a triangle and angles in a quadrilateral?

What are the rules for the angles on a line and angles around a point?

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