Special angles: complementary, supplementary, opposite at a vertex

Complementary angles

Two angles are complementary if the sum of their measures is 90°. Example: an angle of 35° and an angle of 55° are complementary, because 35 + 55 = 90.

Supplementary angles

Two angles are supplementary if the sum of their measures is 180°. Example: an angle of 110° and an angle of 70° are supplementary, because 110 + 70 = 180.

Vertically Opposite Angles

When two lines intersect at a point, they form four angles. The angles that face each other (on either side of the point of intersection) are called vertically opposite angles, and they are always equal in measure.

Example with a mental diagram

Imagine two lines that intersect at O, forming angles a, b, c and d in that order around the point. Therefore:

• a and c are opposite at the vertex -> a = c
• b and d are opposite at the vertex -> b = d
• a and b are supplementary -> a + b = 180

Adjacent angles

Two angles are adjacent if they share the same vertex, have a common side, and lie on either side of that common side (they do not overlap).

Common pitfall

Don’t confuse ‘complementary’ (sum = 90) with ‘supplementary’ (sum = 180). A mnemonic: ‘complementary’ is shorter, just as 90 is smaller than 180. Always check your sum before drawing a conclusion.