Angle Relationships

Complementary Angles

Two angles are complementary if they add up to $90°$.

$\angle A + \angle B = 90°$

If $\angle A = 35°$, then $\angle B = 90° - 35° = 55°$

Supplementary Angles

Two angles are supplementary if they add up to $180°$.

$\angle A + \angle B = 180°$

If $\angle A = 120°$, then $\angle B = 180° - 120° = 60°$

Vertical Angles

When two lines intersect, they form two pairs of vertical angles. Vertical angles are equal.

Adjacent Angles

Angles that share a side and vertex. Adjacent angles on a straight line are supplementary.

Angles in a Triangle

The sum of angles in any triangle is $180°$:

$\angle A + \angle B + \angle C = 180°$

If $\angle A = 50°$ and $\angle B = 70°$: $\angle C = 180° - 50° - 70° = 60°$

Angles with Parallel Lines

When a transversal crosses parallel lines:

• Corresponding angles are equal
• Alternate interior angles are equal
• Co-interior (same-side interior) angles are supplementary

Solving for Unknown Angles

Use algebra! If two supplementary angles are $3x$ and $x + 20$: $3x + (x + 20) = 180$ $4x + 20 = 180$ $4x = 160$ $x = 40°$

So the angles are $120°$ and $60°$.

Practice: Look for angle relationships before writing equations. Vertical angles = equal, linear pair = supplementary.