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Year 5 Maths Angles

Classify angles (acute, right, obtuse, straight, reflex)

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Theory

Angles are named by their size. 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 angle is exactly \(180^\circ\); reflex angles are between \(180^\circ\) and \(360^\circ\); and a full turn is \(360^\circ\). This Year 5 maths page shows each type and how to sort angles into them.

Acute: more than \(0^\circ\) and less than \(90^\circ\).

Right: exactly \(90^\circ\), a quarter turn. Straight: exactly \(180^\circ\), a half turn.

Obtuse: more than \(90^\circ\) and less than \(180^\circ\).

Reflex: more than \(180^\circ\) and less than \(360^\circ\). Full turn (revolution): exactly \(360^\circ\).

Acute, right and obtuse angles Three angles: an acute angle of about 40 degrees, a right angle with a square mark, and an obtuse angle of about 125 degrees. acute right obtuse
Less than \(90^\circ\), exactly \(90^\circ\), between \(90^\circ\) and \(180^\circ\).
Straight and reflex angles Two angles: a straight angle whose arms make a straight line, and a reflex angle of about 230 degrees marked on the outside. straight reflex
Exactly \(180^\circ\); between \(180^\circ\) and \(360^\circ\).

Angle types by size:

\[ \text{acute} < 90^\circ < \text{obtuse} < 180^\circ < \text{reflex} < 360^\circ \]
acute <90< obtuse <180< reflex <360
Exact boundaries. \(90^\circ\) is right (not acute or obtuse); \(180^\circ\) is straight (not obtuse or reflex).
Turns. Quarter turn: right. Half turn: straight. Three-quarter turn: reflex (\(270^\circ\)). Full turn: \(360^\circ\).

How to classify an angle

  1. Is it exactly 90° or 180°? Then it is right or straight.
  2. Less than 90°? Acute.
  3. Between 90° and 180°? Obtuse.
  4. Between 180° and 360°? Reflex.
Example 1 — Name the type
Name each angle.
(i) \(30^\circ\)
(ii) \(115^\circ\)
(iii) \(230^\circ\)
Solution

(i) Acute
(ii) Obtuse
(iii) Reflex

Example 2 — From a description
An angle is \(25^\circ\) more than a right angle. How big is it, and what type is it?
Solution
\(90 + 25\)\(=\)\(115^\circ\)
90+25=115

\(115^\circ\), an obtuse angle.

Example 3 — Short of a straight angle
An angle is \(40^\circ\) less than a straight angle.
(i) How big is it?
(ii) What type is it?
Solution
\(180 - 40\)\(=\)\(140^\circ\)
180−40=140

(i) \(140^\circ\)
(ii) Obtuse

Example 4 — Past a straight angle
An angle is \(50^\circ\) more than a straight angle. What type is it?
Solution
\(180 + 50\)\(=\)\(230^\circ\)
180+50=230

\(230^\circ\) is between \(180^\circ\) and \(360^\circ\), so it is reflex.

Example 5 — Turns
A door swings through a half turn. What type of angle is that, and how many degrees?
Solution
\(360 \div 2\)\(=\)\(180^\circ\)
360÷2=180

A straight angle, \(180^\circ\).

Example 6 — Explain
Why is \(360^\circ\) not a reflex angle?
Solution

Reflex means more than \(180^\circ\) but less than \(360^\circ\). Exactly \(360^\circ\) is a full turn.

Example 7 — Find the mistake
Nia says \(200^\circ\) is obtuse because it is bigger than \(90^\circ\). Explain why she is wrong.
Solution

Obtuse angles must also be less than \(180^\circ\). \(200^\circ\) is more than a straight angle, so it is reflex.

Common pitfalls

Calling 90° acute. Acute is less than \(90^\circ\); \(90^\circ\) is right.
Calling 180° obtuse. Obtuse stops before \(180^\circ\); \(180^\circ\) is straight.
Reading the inside angle when the reflex angle is marked. Look at which side the arc is drawn on.
Judging by arm length. Long arms do not change the size or type of an angle.

Frequently asked questions

What is an acute angle?

An angle less than \(90^\circ\).

What is an obtuse angle?

An angle more than \(90^\circ\) but less than \(180^\circ\).

What is a reflex angle?

An angle more than \(180^\circ\) but less than \(360^\circ\).

What type of angle is 300°?

Reflex: it is more than \(180^\circ\) but less than \(360^\circ\).

What type of angle is a three-quarter turn?

Reflex: it is \(270^\circ\).

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