When two lines intersect, the opposite angles are called vertical angles, and vertical angles are equal. Also, the sum of angles on a straight line is 180°.
Example ①
Two lines intersect, and one of the angles is 65°. Find the vertical angle and the adjacent angle.
Answer: Vertical angle = 65° (they are equal). Adjacent angle = 180°−65° = 115°
Two lines intersect, and one of the angles is 65°. Find the vertical angle and the adjacent angle.
Answer: Vertical angle = 65° (they are equal). Adjacent angle = 180°−65° = 115°
Key Points
- Vertical angles: Opposite angles at the intersection of two lines → equal
- Sum of angles on a straight line = 180°
- Sum of angles around one point = 360°
Practice Problem
- Two lines intersect, and one of the angles is 40°. Find all of the remaining three angles.
Answer and Explanation
- Answer: Vertical angle 40°, adjacent angles 140° (×2). Vertical angles are equal, and each adjacent angle is 180°−40°=140°.