Acute and obtuse
🎯 In this topic you will
- Learn the correct names used to describe angles of different sizes.
🧠 Key Words
- acute angle
- obtuse angle
- right angle
Show Definitions
- acute angle: An angle that is smaller than a right angle and measures less than 90°.
- obtuse angle: An angle that is larger than a right angle but smaller than a straight angle, measuring between 90° and 180°.
- right angle: An angle that measures exactly 90°, forming a square corner.
Talking About Shapes Clearly
I t is important to be able to talk about shapes and movements accurately.
New Words for Angles
I n this section you will learn some new words for describing angles.
❓ EXERCISES
$1.$ Make an angle maker. You will need: card, tracing paper, a ruler, a split pin (or a drawing pin and a small piece of modelling dough). Trace and copy the diagram carefully onto a piece of card. Make a thin rectangle out of card. Attach the thin rectangle to the diagram with a split pin, or push a drawing pin through the rectangle and diagram into modelling dough. Use your angle maker to make:
a. a right angle
b. an acute angle
c. an obtuse angle
👀 Show answer
a. A right angle is made when the moving rectangle lines up with the vertical dashed line, giving an angle of $90^\circ$.
b. An acute angle is made when the moving rectangle is between $0^\circ$ and $90^\circ$, that is, smaller than a right angle.
c. An obtuse angle is made when the moving rectangle is between $90^\circ$ and $180^\circ$, that is, larger than a right angle but less than two right angles.
❓ EXERCISES
$2.$ Write right angle, acute angle or obtuse angle for each angle.
👀 Show answer
a. Acute angle
b. Obtuse angle
c. Obtuse angle
d. Right angle
e. Obtuse angle
$3.$
a. Draw an acute angle.
b. Draw an obtuse angle.
👀 Show answer
a. An acute angle is any angle less than $90^\circ$.
b. An obtuse angle is any angle greater than $90^\circ$ and less than $180^\circ$.
$4.$ Copy and complete these sentences.
A right angle is an angle of ____ degrees.
An acute angle is ____ than ____.
An obtuse angle is ____ than ____ and ____ than ____.
👀 Show answer
A right angle is an angle of $90$ degrees.
An acute angle is less than $90^\circ$.
An obtuse angle is more than $90^\circ$ and less than $180^\circ$.
🧠 Think like a Mathematician
Maryam has drawn an obtuse angle.
She is drawing a line with a ruler to cut the angle into two angles.
Maryam says, ‘If I draw a straight line through an obtuse angle I always get two acute angles.’
Conjecture whether Maryam is correct.
Investigate and find out. Then convince yourself of your answer.
👀 show answer
Maryam is not always correct.
An obtuse angle is greater than $90^\circ$ and less than $180^\circ$. When a straight line is drawn through it, the two new angles must add up to the original obtuse angle.
It is possible to draw the line so that:
- one angle is acute (less than $90^\circ$)
- and the other angle is obtuse (greater than $90^\circ$).
Only if the line is drawn very close to the middle will both angles be acute, but this does not happen every time.
Therefore, drawing a straight line through an obtuse angle does not always give two acute angles.