Angles in a Triangle

≈ 25 min

The three interior angles of any triangle always add up to $180^\circ$ . This single fact lets you find a missing angle whenever you know the other two:

\text{missing angle} = 180^\circ - (\text{angle}_1 + \text{angle}_2)

Some special triangles: an equilateral triangle has three equal angles, so each is $180^\circ \div 3 = 60^\circ$ . A right-angled triangle has one $90^\circ$ angle, leaving $90^\circ$ to share between the other two.

Worked example. Two angles of a triangle are $40^\circ$ and $75^\circ$ . The third is $180^\circ - (40^\circ + 75^\circ) = 65^\circ$ .

The three interior angles of a triangle always add up to…

$90^\circ$

$180^\circ$

$270^\circ$

$360^\circ$

Two angles of a triangle are $50^\circ$ and $60^\circ$ . Find the third angle, in degrees.

Each angle of an equilateral triangle is how many degrees?

A right-angled triangle has a $90^\circ$ angle and a $35^\circ$ angle. Find the third angle, in degrees.