Lesson 1: Adjacent and Vertical Angles

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

When adjacent angles combine to form a larger angle, their measures add together: $\text{angle}_1 + \text{angle}_2 = \text{total angle}$. If the adjacent angles form a straight line, then $\text{angle}_1 + \text{angle}_2 = 180°$. If the adjacent angles form a right angle, then $\text{angle}_1 + \text{angle}_2 = 90°$.

Examples