Lesson Guide
Explanation
So far you have sorted angles by comparing them to a right angle: smaller, the same, or bigger. Now you can put an actual number on them. A full turn is 360 degrees, which means a quarter turn — a right angle — is 90 degrees, and a half turn, a straight angle, is 180 degrees. Once you have numbers you can say not just that an angle is bigger, but exactly how much bigger.
Your Turn
A quarter turn is 90 degrees. How many degrees is three quarters of a turn? Check: 270 degrees.
Watch Out
A full turn is 360 degrees, not 100. It is an old number from ancient astronomy, and it is worth memorising.
Explanation
Angles get names according to their size. Under 90 degrees is acute — a sharp, narrow angle. Exactly 90 is a right angle. Between 90 and 180 is obtuse, a wide open angle. Exactly 180 is straight, a flat line. And then there is the one you have not met: bigger than 180 but less than a full turn is called reflex. A reflex angle looks like it is bending backwards on itself, and it is the outside of an angle rather than the inside.
Your Turn
Name these: 30 degrees, 100 degrees, 250 degrees. Check: acute, obtuse, reflex.
Watch Out
Acute and obtuse are easy to swap. Acute is the small, sharp one — think of a cute little angle.
Explanation
Here is the key idea. Between two arms there are really two angles: the small one inside, and the big one going the other way round the outside. The small one here is 70 degrees. The reflex angle is the rest of the full turn, which is 360 minus 70, or 290 degrees. The two always add up to 360 because together they go all the way round. So you never really measure a reflex angle directly — you measure the small one and subtract from 360.
Your Turn
The angle inside is 110 degrees. What is the reflex angle outside it? Check: 360 minus 110 = 250 degrees.
Watch Out
Subtract from 360, not from 180. A full turn is 360, and reflex angles live in the space above 180.
Explanation
A protractor measures angles, and there are three steps. Put the little centre hole exactly on the corner of the angle. Line one arm up with the zero line. Then read where the other arm crosses the scale. The catch is that a protractor has two scales, one running each way, and it is easy to read the wrong one. The fix is simple: use the scale that starts at zero on your arm, and sanity-check against what you already know — if the angle clearly looks smaller than a right angle, the answer must be under 90.
Your Turn
An angle looks a bit wider than a right angle and the protractor shows either 60 or 120. Which is it? Check: 120, because it must be more than 90.
Watch Out
Reading the wrong scale gives 60 instead of 120. Always ask whether the angle looks bigger or smaller than a right angle first.
Explanation
A normal protractor only goes up to 180 degrees, so you cannot measure a reflex angle directly — there simply is not enough scale. Instead you measure the small angle on the inside, then subtract it from 360. If the small angle is 85 degrees, the reflex angle is 360 minus 85, which is 275 degrees. Always check the answer is sensible: a reflex angle must be between 180 and 360, so if you get 95 you have made a mistake somewhere.
Your Turn
The small angle measures 140 degrees. What is the reflex angle? Check: 360 minus 140 = 220 degrees.
Watch Out
Your answer must land between 180 and 360. Anything outside that range is not a reflex angle at all.
📌 Key Points — this lesson in a nutshell
- A full turn is 360 degrees; a right angle is 90; a straight angle is 180.
- Acute < 90, right = 90, obtuse is 90 to 180, straight = 180, reflex is 180 to 360.
- The inside angle and its reflex always add to 360.
- Protractor: centre on the corner, one arm on zero, read the scale starting at zero.
- To measure a reflex angle, measure the small one and subtract from 360.
Step 1: Introduction
Step 1 of 5
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