Angles
“An angle is how wide two sides open.”
The hook
A door swinging open, a clock hand turning — an angle measures how much something has opened or turned.
In plain words
How far apart two lines (sides) spread from one point. We measure that spread in degrees (°).
The intuition
Two sides together is 0 degrees; a full turn is 360. When two sides meet in a clean corner, that's a right angle = 90 degrees. Opened flat into a line is a straight angle = 180. An angle is 'how much of a turn'.
How it's built
An angle has a vertex (the meeting point) and two sides. We measure it with a protractor. Below 90° it's acute, exactly 90° is right, between 90° and 180° is obtuse.
Example
At 3 o'clock, the two clock hands make a right angle — 90 degrees.
Common mistake
An angle's size has nothing to do with how long you draw the sides. Longer sides with the same opening still make the same angle.
Where it's used
Directions (turn so many degrees), designing buildings and furniture, sports (the angle of a kick) — anywhere shape and direction matter.
Where it came from
Splitting a full turn into 360 degrees is said to come from the base-60 counting of ancient Babylon.
Quick check
How many degrees is a right angle (a square corner)?
- 45°
- 90°✓
- 180°
- 360°
Practice
How many degrees is a straight angle (a flat line)?
Answer: 180
- It's two right angles joined.
- 90 + 90 = 180
- → 180°
Takeaway: A flat line makes a 180° angle.
Half of a right angle is how many degrees?
Answer: 45
- Right angle = 90°
- 90 ÷ 2 = 45
- → 45°
Takeaway: Half of 90° is 45°.
At 3 o'clock, how many degrees is the angle between the clock hands?
Answer: 90
- From 12 to 3 is a quarter turn.
- 360 ÷ 4 = 90
- → 90° (a right angle)
Takeaway: A quarter turn is 90°.