Skip to content
VirtusAcademy

Types of Angle

FoundationAQAEdexcelOCR

Master types of angle for GCSE Maths with structured, exam-style practice. This Foundation resource covers identifying types of angle and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Acute is under 90°, obtuse 90°–180°, reflex over 180°.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Topic overview

Angles are classified by size, and knowing the names lets you describe and check your answers quickly.

An acute angle is less than \(90^\circ\), a right angle is exactly \(90^\circ\), and an obtuse angle is between \(90^\circ\) and \(180^\circ\). A straight line makes \(180^\circ\), and a reflex angle is more than \(180^\circ\) but less than \(360^\circ\).

The names are useful as a sense-check. If a question describes an obtuse angle and your working gives \(40^\circ\), you know immediately that something has gone wrong, which often catches an error before you write the answer down.

Revision notes

The five types

Acute is under \(90^\circ\), right is exactly \(90^\circ\), obtuse is between \(90^\circ\) and \(180^\circ\), straight is \(180^\circ\), and reflex is over \(180^\circ\).

A right angle is usually marked with a small square rather than an arc, which is worth recognising on diagrams.

Measuring with a protractor

Line up the centre of the protractor on the vertex and the zero line along one arm, then read where the other arm crosses.

Protractors have two scales, so decide first whether the angle is acute or obtuse and pick the reading that matches.

Reflex angles

A reflex angle is measured the long way round. Measure the smaller angle and subtract from \(360^\circ\).

If the acute angle is \(70^\circ\), the reflex angle at the same point is \(360 - 70 = 290^\circ\).

Key points

  • Acute angles are less than \(90^\circ\).
  • A right angle is exactly \(90^\circ\).
  • Obtuse angles are between \(90^\circ\) and \(180^\circ\).
  • A straight line is \(180^\circ\).
  • Reflex angles are between \(180^\circ\) and \(360^\circ\).
  • Use the type as a check on your answer.

Worked examples

Example 1

Name the type of angle measuring \(130^\circ\).

Working

\[130 \text{ is between } 90 \text{ and } 180\]compare with the boundaries
\[\text{Obtuse}\]name the type

Example 2

Find the reflex angle when the acute angle is \(55^\circ\).

Working

\[360 - 55\]angles at a point add to 360 degrees
\[= 305^\circ\]state the reflex angle

Example 3

Name the type of angle measuring \(90^\circ\).

Working

\[\text{Exactly } 90^\circ\]compare with the definitions
\[\text{A right angle}\]name the type

Common mistakes

  • Calling a \(90^\circ\) angle acute.

    Acute means strictly less than 90 degrees. Exactly 90 is a right angle.

  • Reading the wrong protractor scale.

    Decide whether the angle is acute or obtuse first, then choose the matching scale.

  • Measuring a reflex angle directly.

    A protractor only reaches 180 degrees, so measure the smaller angle and subtract from 360.

  • Not checking the answer against the angle type.

    If the diagram shows an obtuse angle, your answer must be over 90 degrees.

Exam tips

  • Use the angle type as a quick sense-check on every answer.
  • Decide acute or obtuse before reading a protractor.
  • Look for the small square marking a right angle on diagrams.
  • Subtract from 360 to find a reflex angle.

Key terms

Acute
An angle less than \(90^\circ\).
Obtuse
An angle between \(90^\circ\) and \(180^\circ\).
Reflex
An angle between \(180^\circ\) and \(360^\circ\).
Vertex
The point where two arms of an angle meet.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.