Angles of an equilateral triangle
All three angles of an equilateral triangle are 60°.
Three equal sides
The school logo is an equilateral triangle: all three sides are equal. Meera says: “Then all three angles must be equal too.” Rabia asks: “And how big is each angle?”
How big is each angle of an equilateral triangle?
What this lesson covers
The idea
All sides of an equilateral triangle are equal, so all three of its angles are equal, and since they add up to 180°, each angle is 60°.
Three equal sides
The school logo is an equilateral triangle: all three sides are equal. Meera says: “Then all three angles must be equal too.” Rabia asks: “And how big is each angle?”
How big is each angle of an equilateral triangle?
- 60°
- 90°
- It depends on the size
Look from each corner
Tap a corner and take it as the top of the triangle. Its two sides are equal, so the angles at the other two corners are equal. Do it for all three corners. Then fit the three angles on a straight line.
All three angles are equal, and 60°
From corner A: ∠B = ∠C. From corner B: ∠A = ∠C. From corner C: ∠A = ∠B. So ∠A = ∠B = ∠C. Three equal angles add up to 180°, so each is 180° ÷ 3 = 60°.
The angles of an equilateral triangle are all equal, since all its sides are equal. As the angles add up to 180°, each angle of an equilateral triangle is 60°.
- Corner on top | Equal sides | Equal angles
- A | AB = AC | ∠B = ∠C
- B | BA = BC | ∠A = ∠C
- C | CA = CB | ∠A = ∠B
Notes
The angles of an equilateral triangle are all equal, since all its sides are equal. As the angles add up to 180°, each angle of an equilateral triangle is 60°.
Check yourself
An equilateral triangle has sides of 7 cm. How big is each of its angles, in degrees?
Answer: 60
All three angles are equal and add up to 180°, so each is 180° ÷ 3 = 60°. The size of the sides does not matter.
Meera says: “A big equilateral triangle has bigger angles than a small one.” Is she right?
Why is each angle of an equilateral triangle 60°?
∆ABC has AB = BC = CA. Which of these is true?
- No. Every equilateral triangle has three angles of 60°. — correct. Yes! The angles are 60° whatever the size.
- Yes, bigger triangles have bigger angles. The size of the sides does not change the angles.
- Yes, but only if the sides are longer than 10 cm. There is no such rule. Every equilateral triangle has 60° angles.
- Because the sides are 60 cm. The sides can be any length. The angles are 60° for every size.
- Because one angle is a right angle. None of its angles is a right angle. Each is 60°.
- Because the three angles are equal and add up to 180° — correct. Yes! 180° ÷ 3 = 60°.
- ∠A is bigger than ∠B. All three angles are equal.
- ∠A = 90°. Each angle is 60°, so ∠A is not 90°.
- ∠A = ∠B = ∠C = 60° — correct. Yes! Equal sides give equal angles, and they add up to 180°.