Triangles by Angles

Today's big idea

By angles: Acute (all <90°), Right (one =90°), Obtuse (one >90°).

One corner over 90° is enough to settle the name, and no triangle can hold two.

How it works

👀 What's going on?

Look at a slice of pizza, then at a set square. Both are triangles, yet they feel nothing alike. The difference lives in the corners, not in the sides.

💡 Here's the trick

Look at the diagram above. The largest angle on its own decides the name of a triangle. All three under 90° makes an acute triangle. Exactly one angle of 90° makes a right triangle. One angle over 90° makes an obtuse triangle.

🪄 How to do it

1.Read all three angles from the diagram above.
2.Pick out the largest of the three angles.
3.Under 90° is acute, at 90° is right, over 90° is obtuse.

✍️ Try it

A triangle has angles 70°, 65° and 45°. Which type is it? Then: another triangle has two angles of 25° and 45°. Which type is that one?

Every angle in the first is below 90°, so it is acute. In the second the third angle is 180 − 25 − 45 = 110°, so it is obtuse.

⚠️ Watch out

You might be thinking that a triangle could hold two right angles. Two right angles already use up the whole 180°, leaving nothing for the third corner. For the same reason no triangle can hold two obtuse angles either.

🌟 Why this matters

A ladder leaning on a wall makes a right triangle, and a wide tent flap makes an obtuse one. Carpenters trust a set square because a true square corner keeps every shelf level. Knowing the largest angle tells you the shape before you draw a thing.
Exam tip: Add the two angles you are given, subtract from 180°, then choose the name.

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“A triangle has angles 100°, 50°, 30°. What TYPE by angles?”

1
Find the biggest angle
100° is the largest. 📐
2
Compare with 90°
100 > 90 → obtuse.
3
Pick the type
One angle over 90° → obtuse triangle.
4
Answer ✓
The triangle is obtuse.

Now you try one — same steps, different story 👇

See it in action

⚡ Time to play!

Look at the BIGGEST angle: all < 90° = acute, one = 90° = right, one > 90° = obtuse.

ANGLE SORT · ROUND 1 OF 2 · SORT ALL 6

Quick check

✅ VERIFICATION

Which set of angles can form an obtuse triangle?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Quadrilaterals

Six shapes, angles sum to 360°.

Concept 5 of 9 →