Acute and obtuse angles

Not every angle is exactly a right angle. Some are smaller , like the angle between the open jaws of a pair of scissors at the start of a snip. Some are bigger , like the angle of a fan-leaf almost folded back. These have special names: acute and obtuse.

What is this?

An acute angle is smaller than a right angle. Less than a quarter turn. Less than 90°. Acute angles look "sharp" or "narrow" , like the tip of a pencil, the corner of a samosa, or the angle between an open book's two halves when it is only slightly open.

An obtuse angle is bigger than a right angle but smaller than a half turn. Between 90° and 180°. Obtuse angles look "wide" , like a slice of pizza that takes up almost a third of the pizza, or the angle of a relaxing camp-chair's back.

And the straight angle is exactly a half turn. 180°. Both arms point in exactly opposite directions. The two arms together look like a straight line.

To check if an angle is acute or obtuse, just compare it to a right angle:

• Smaller than the corner of your paper? Acute.
• Same as the corner? Right angle.
• Bigger than the corner but not yet a straight line? Obtuse.
• Looks like a straight line? Straight angle.

The hands of a clock can show all four. At 1 o'clock they form an acute angle. At 3 o'clock, a right angle. At 4 o'clock, an obtuse angle. At 6 o'clock, a straight angle.

Worked examples

Example 1. At 2 o'clock, the hour hand and minute hand make what kind of angle?

• From 12 to 2 on the clock face is less than a quarter of the way round.
• The angle is smaller than 90° → acute.

Example 2. At 5 o'clock, what kind of angle do the two hands make?

• From 12 to 5 is more than a quarter but less than half of the way round.
• The angle is bigger than 90° but less than 180° → obtuse.

Example 3. Look at the corner where two adjacent triangles of a kite meet. The angle is wider than the corner of a book. What is it?

• Wider than a right angle → obtuse.

Try it

1. Draw an acute angle.
2. Draw an obtuse angle.
3. The angle at the tip of an open pair of scissors is small. What kind of angle is it?
4. Is the angle at 4 o'clock acute or obtuse?
5. Sort: 30°, 90°, 120°, 75°, 180° → which are acute, right, obtuse, straight?

Hands-on

Hand fan. Take a folding hand-fan (or a folded paper fan). Open it a little , see the acute angle. Open it more , until the two ends are at right angles. Open further , that is obtuse. Open all the way , that is a straight angle.

Living-room angles. Take a paper "right-angle checker" (the corner of any paper). Spot 3 acute angles and 3 obtuse angles in your living room. Note them down.