Vertically opposite angles
Objective. Identify and use equal vertically opposite angles.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Vertically opposite angles are formed when two straight lines cross, creating two pairs of equal angles directly across from each other at the intersection. These angles are always equal because each pair shares the same two lines and the same amount of turn. For example, if two lines cross and one angle is 72°, the angle directly opposite it is also 72°, while the two angles adjacent to it on the straight line are each 108°, since angles on a line sum to 180°. Spotting vertically opposite angles quickly helps solve more complex angle problems involving intersecting lines.
Worked example
Two straight lines cross, forming an angle of 58° on one side. Use vertically opposite angles to find the angle directly across from it.
- 1Identify the given angle: 58°.
- 2Recall that vertically opposite angles are always equal.
- 3The angle directly opposite the 58° angle must also be 58°.
- 4Check the adjacent angles on the straight line sum to 180°: 180−58=122°, confirming consistency.
Answer: 58°
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes assume all four angles formed by crossing lines are equal, rather than just the two opposite pairs. Check carefully which angles are directly across from each other before assuming equality.
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