The biggest angle decides
Acute-angled, right-angled and obtuse-angled triangles.
How big can an angle get?
The three angles of a triangle add up to 180°. Think about its biggest angle.
Can a triangle have an angle bigger than 90°?
What this lesson covers
The idea
Based on angle measures, a triangle is acute-angled if all three angles are acute, right-angled if it has one right angle, and obtuse-angled if it has one obtuse angle.
How big can an angle get?
The three angles of a triangle add up to 180°. Think about its biggest angle.
Can a triangle have an angle bigger than 90°?
- No, never
- Yes, but only one such angle
- Yes, and it can have two or three
Reshape the triangle
Drag A and watch the three angles. Make all three kinds.
Naming by angles
A triangle gets its name from its angles.
A triangle cannot have two right angles or two obtuse angles: they would already add up to 180° or more, with nothing left for the third angle. So every triangle has at least two acute angles. That is why “acute-angled” needs all three angles acute.
Based on angles, a triangle is acute-angled if all three angles are acute, right-angled if it has one right angle, and obtuse-angled if it has one obtuse angle.
- Name | Its angles
- Acute-angled | all three angles are acute (less than 90°)
- Right-angled | one angle is a right angle (90°)
- Obtuse-angled | one angle is obtuse (more than 90°)
Notes
Based on angles, a triangle is acute-angled if all three angles are acute, right-angled if it has one right angle, and obtuse-angled if it has one obtuse angle.
Check yourself
A triangle has angles 50°, 60° and 70°. What kind of triangle is it?
A triangle has angles 30°, 40° and 110°. What kind of triangle is it?
How many acute angles does an obtuse-angled triangle have?
Answer: 2
The obtuse angle is more than 90°, so the other two together are less than 90°. Both are acute: that is 2 acute angles.
Rina says: “My triangle has an acute angle, so it is acute-angled.” Is she right?
- Right-angled. None of the angles is 90°.
- Acute-angled — correct. Yes! All three angles are less than 90°.
- Obtuse-angled. None of the angles is more than 90°.
- Acute-angled. Acute-angled needs all three angles less than 90°. Here one angle is 110°.
- Obtuse-angled — correct. Yes! One angle, 110°, is more than 90°.
- Right-angled. None of the angles is exactly 90°.
- Yes. One acute angle makes it acute-angled.. It needs all three angles acute. A right-angled triangle also has acute angles.
- Yes, as long as it has no right angle.. An obtuse-angled triangle has no right angle, and it is still not acute-angled.
- No. Acute-angled needs all three angles acute. Every triangle has acute angles, even a right-angled one. — correct. Yes! Every triangle has at least two acute angles, so one acute angle proves nothing.