Concept 3 of 6
Sorting Triangles by Angles
Today's big idea
Sort a triangle by its biggest angle, because that one alone decides the name.
Under 90° is acute, exactly 90° is right, and over 90° is obtuse.
How it works
👀 What's going on?
The very same triangle can be sorted a second way, by its corners instead of its sides. One corner is enough to settle the name.
💡 Here's the trick
Look at the three corners above. If every angle is under 90° the triangle is acute. If one is exactly 90° it is right. If one is over 90° it is obtuse. Only one angle can ever reach 90° or more, because all three still have to add up to 180°.
🪄 How to do it
- 1.Check each of the three corners, as the picture above marks them.
- 2.Find the biggest angle, because that single one decides everything.
- 3.Under 90° is acute, exactly 90° is right, and over 90° is obtuse.
✍️ Try it
One triangle has angles of 120°, 30° and 30°. Another has 60°, 60° and 60°. Name each one by its angles.
The 120° corner is over 90°, so that triangle is obtuse. All three angles of the second are under 90°, so it is acute. That second one is also equilateral, which shows sides and angles are two separate labels.
⚠️ Watch out
You might be thinking a triangle could have two right angles. It cannot. Two 90° corners already use up the entire 180°, leaving nothing at all for the third.
🌟 Why this matters
Ramps, roof pitches and the lean of a ladder are all chosen by angle. A right angle in particular is what lets a corner sit flat against a wall.
Exam tip: Find the biggest angle first, because it alone settles which of the three names applies.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A triangle has angles 70°, 60°, and 50°. What type?”
- 1
Look at each angle
70°, 60°, 50°.
- 2
Any 90° or bigger?
The biggest is 70° — every angle is under 90°.
- 3
Match the rule
All angles < 90° = acute.
- 4
Answer ✓
It's acute
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Look at each triangle's angles. Tap the correct angle label for each one!
Angles: 90° + 45° + 45°
Angles: 120° + 30° + 30°
Angles: 60° + 60° + 60°
Quick check
✅ VERIFICATION
A triangle has angles of 100°, 45° and 35°. Name it by its angles.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Compound Perimeter
Compound shape? Walk every edge, add them up.