The theorem

For any triangle with interior angles $A$, $B$, and $C$:

$$A + B + C = 180°$$

Why it works (intuition)

Draw a line through one vertex parallel to the opposite side. The other two angles of the triangle reappear at that vertex as alternate-interior angles — and together with the third angle they form a straight line.

Application: isosceles triangles

An isosceles triangle has two equal sides; the angles opposite those sides are also equal.

If the apex angle is $40°$, the base angles each measure:

$$\frac{180° - 40°}{2} = 70°$$

Common trap

Students sometimes assume any triangle that "looks isosceles" actually is. Always justify equal angles from given equal sides — or vice versa.