Angles On A Straight Line Worksheet

Angles on a straight line at a glance

Measuring angles with a protractor on a scale diagram is one way to find the size of unknown angles. However, a more efficient method is to use known angle facts when finding missing angles or calculating angles in 2D shape problems. 

Angles on a straight line sum to 180°, so if, for example, we know that acute angle ‘a’ and obtuse angle ‘b’ lie on a straight line, and we know the size of angle ‘a’, we can find the size of angle ‘b’ by subtracting angle ‘a’ from 180°. 

A special case of this rule is pairs of angles whose sum is 180° – these are called supplementary angles (this terminology is not required at GCSE, but the idea is useful). 

Sometimes a missing angle problem might include a right angle, marked with the ∟ symbol. This can confuse students, so it’s important they recognise the symbol for a right angle, use subtraction from 180° to leave 90°, and then use other information to solve to find the unknown angle.

The fact about angles on a straight line can be extended further to 2D shape problems requiring students to solve an equation to find unknown angles. 

Looking forward, students can then progress to additional angles rules worksheets and other geometry worksheets, for example an angles in polygons worksheet or volume and surface area of spheres worksheet.

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.