Lesson 1: Angle Relationships and Construction

Property

When two line segments meet at a point, they form an angle. The point where the two sides meet is called the vertex.

• If the sides are less open than a right angle, we call the angle acute.
• If the sides are more open than a right angle, we call the angle obtuse.
• If the two sides are totally open to form a straight line, we call the angle a straight angle.
• In a right angle, the sides are perpendicular.

Examples

• The tip of a slice of pie typically forms an acute angle.
• At 5:00, the hands of a clock form an obtuse angle.
• A perfectly straight pencil lying on a desk represents a straight angle.

Property

Adjacent angles are two angles that share a common vertex and a common side, but have no interior points in common. If angles $\angle ABC$ and $\angle CBD$ are adjacent, they share vertex $B$ and common side $\overrightarrow{BC}$.

Examples

Property

If the sum of the measures of two angles is 180°, then the angles are supplementary.

If the sum of the measures of two angles is 90°, then the angles are complementary.

Examples

• An angle measures 70°. Its supplement is 180° - 70° = 110° because supplementary angles must add up to 180°.
• An angle measures 35°. Its complement is 90° - 35° = 55° because complementary angles must add up to 90°.