Concept 4 of 6
The Missing Slice: Angle Detective Work
Today's big idea
Pick the right total, then subtract the angles you already know from it.
Match the total to the setup: a line is 180°, a full turn 360°, a corner 90°.
How it works
👀 What's going on?
Two rays meet at a point and open apart. The amount they open is the angle, measured in degrees, and a question will often hand you every angle except one.
💡 Here's the trick
Look at the circle above. It is cut into 120°, 90° and one unknown slice. A full turn is always 360°. The two known slices come to 210°, so the missing one has to be 360 − 210 = 150°. Every missing-angle puzzle is that subtraction, once you know which total to use.
🪄 How to do it
- 1.Decide the total, as the picture above uses 360° for a full circle.
- 2.Add up every angle you have been given.
- 3.Subtract that sum from the total to get the missing angle.
✍️ Try it
A straight line splits into 65° and one unknown. Then a right angle splits into 25° and one unknown. Which total does each one use?
A straight line is 180°, so the first missing angle is 180 − 65 = 115°. A right angle is 90°, so the second is 90 − 25 = 65°. The same subtraction both times, but the wrong total wrecks it.
⚠️ Watch out
You might be thinking every missing angle subtracts from 360°. Only a full turn is 360°. Use 180° along a straight line and 90° inside a right angle, or that 65° answer comes out as 295°.
🌟 Why this matters
A pizza cut into uneven slices, the hands of a clock, the tilt of a skateboard ramp. All of them are angles adding up to a total you already know.
Exam tip: Look for a mark or a straight edge in the figure, because it tells you which total to use.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A straight line (180°) is split into 65° and ?. Find the missing angle.”
- 1
What's the total?
A straight line = 180°.
- 2
Add the knowns
Only 65° is used so far.
- 3
Subtract from total
180 − 65 = 115
- 4
Missing piece ✓
Missing angle = 115°
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
CHALLENGE 1 OF 3
Make a right angle (90°)
Quick check
✅ VERIFICATION
A full circle is split into 100°, 130° and one more slice. How big is the missing slice?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Angle Sum
Know two angles? Subtract from 180° to find the third.