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Year 4 Maths Angles

Classify angles (acute, right, obtuse)

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Theory

Classifying angles is a Year 4 maths geometry skill: sorting angles into acute, right, obtuse and straight by comparing each opening to a right angle (a square corner). This page explains how a right angle is a quarter turn, how a straight angle is a half turn, and how to name any angle, including the angles of clock hands and the corners of shapes. In Western Australia this is taught in Year 5. Curriculum: VC2M4M04 / AC9M4M04.

An angle is the amount of turn between two arms that meet at a point. We name an angle by comparing its opening to a right angle, which is a square corner like the corner of a book or a page.

An acute angle opens less than a right angle. A right angle is exactly a square corner. An obtuse angle opens more than a right angle but less than a straight angle. A straight angle is a half turn, where the two arms make a straight line.

The length of the arms does not change the angle. Only the size of the opening tells you the type. Two angles can be the same size even if one is drawn with much longer arms.

Acute angle and right angle A small acute angle beside a right angle. The acute angle opens less than the square corner of the right angle, which is marked with a small square. Acute Right
An acute angle opens less than a right angle. The small square marks the right angle.
Obtuse angle and straight angle A wide obtuse angle beside a straight angle. The obtuse angle opens more than a right angle, and the straight angle is a half turn along a straight line. Obtuse Straight
An obtuse angle opens more than a right angle. A straight angle is a half turn along a straight line.

These angle facts are worth remembering. Every angle can be named by comparing it to a right angle.

\[ \text{right angle} = \dfrac{1}{4}\text{ of a full turn} \]
right angle =14 turn
\[ \text{straight angle} = \dfrac{1}{2}\text{ turn} = 2 \text{ right angles} \]
straight angle =12 turn =2 right angles
Angle typeHow much it opens
AcuteLess than a right angle
RightExactly a right angle (a square corner)
ObtuseMore than a right angle, less than a straight angle
StraightA half turn (two right angles in a line)
Order of size. From smallest to largest the angle types go acute, then right, then obtuse, then straight. A right angle is the square corner you check every other angle against.

How to classify any angle

  1. Find the corner. Look at the point where the two arms meet, not at how long the arms are.
  2. Compare to a right angle. Picture a square corner, or fit the corner of a book or paper into the angle.
  3. Name it. Less than a square corner is acute, exactly a square corner is right, more than a square corner but not a straight line is obtuse, and a straight line is a straight angle.

How to classify the corners of a shape

  1. Go around the shape. Visit each corner once.
  2. Name each corner. Use the steps above for every corner.
  3. Tally the types. Count how many corners are acute, right and obtuse. The tallies add up to the number of corners.
Example 1 — Name four angles
Classify each angle \(A\), \(B\), \(C\) and \(D\) as acute, right, obtuse or straight.
Four angles A, B, C and D Angle A opens wider than a square corner, angle B opens only a little, angle C is a straight line through its vertex, and angle D has a small square marking a right angle. A B C D
Solution

\(A\) opens more than a square corner but is not a straight line, so it is obtuse.

\(B\) opens less than a square corner, so it is acute.

\(C\) makes a straight line through its vertex, so it is a straight angle.

\(D\) has the small square, so it is a right angle.

Example 2 — Clock angles
Classify the angle between the hands of a clock at 2 o'clock, and at 4 o'clock.
Clocks showing 2 o'clock and 4 o'clock Two clock faces. At 2 o'clock the hands make a small angle. At 4 o'clock the hands make a wide angle that is more than a square corner but less than a straight line. 12 2 o'clock 12 4 o'clock
Solution

At 2 o'clock the hands open less than a square corner, so the angle is acute.

At 4 o'clock the hands open more than a square corner but do not make a straight line, so the angle is obtuse.

Example 3 — Corners of a shape
This slanted four-sided shape is a parallelogram. How many of its corners are acute, right and obtuse?
A parallelogram with its corners marked A slanted four-sided shape. Two opposite corners are sharp and two opposite corners are wide. A red arc marks each corner.
Solution

Go around the shape and check each corner.

Two corners are sharp (less than a square corner): \(2\) acute.

Two corners are wide (more than a square corner): \(2\) obtuse.

No corner is square: \(0\) right angles. Check: \(2 + 0 + 2 = 4\) corners.

Example 4 — Everyday angles
Classify each angle.
(i) The point at the top of a tall tent.
(ii) The corner of a window frame.
(iii) The back of a deck chair leaning far back from the seat.
Solution

(i) The tent sides meet in a sharp point: acute.

(ii) A window frame has square corners: right angle.

(iii) The chair back opens wider than a square corner but not flat: obtuse.

Common pitfalls

Long arms do not make a bigger angle. Watch out for judging an angle by the length of its arms. Two angles can open the same amount even if one has much longer arms. Look only at the turn between them.
A square corner is a right angle. If a book or paper corner fits the angle exactly, it is a right angle, not acute or obtuse.
A straight angle is still an angle. It looks like a straight line, but the two arms point opposite ways from one point. That is a half turn.

Frequently asked questions

How can I remember acute and obtuse?

Think of acute as a small, sharp angle, smaller than a square corner. Obtuse is a wide, open angle, bigger than a square corner but not yet a straight line.

What is a right angle?

A right angle is a square corner, like the corner of a book or a page. It is a quarter turn. We mark it with a small square.

Is a straight angle really an angle?

Yes. A straight angle is a half turn. The two arms point in opposite directions from one point and make a straight line.

How can you tell if an angle is a right angle?

Fit a square corner, such as the corner of a book or a piece of paper, into the angle. If it fits exactly with no gap and no overlap, the angle is a right angle.

Can one shape have different types of angles?

Yes. A parallelogram that leans over has two acute corners and two obtuse corners. Check each corner on its own.

Do I need to measure angles to classify them?

No. You classify an angle by comparing it with a right angle. Measuring angles with a protractor comes in later years.

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