A triangle's angles always sum to 180°

The fact to remember

No matter the shape: a triangle’s three angles together always add up to 180°. Here’s the quickest visual proof.

Proof in 3 moves

Étape 1 / ?

Any triangle with its 3 angles A, B, C.

We « detach » the three angles in our mind.

Stick them side by side: they form a straight line. A straight line is 180°.

If you know two angles, the third comes from one subtraction:

$\text{Third angle} = 180° - (\text{first} + \text{second})$

In a right triangle, one angle is already 90°. So the other two share the remaining 90° — they are complementary.

?Your turn

In a triangle, two angles measure 47° and 68°. What's the third?