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what are vertical angles

Vertical angles are pairs of opposite angles formed when two straight lines intersect, and each pair always has equal measure.

What are vertical angles?

When two straight lines cross, they make an “X” shape and form four angles at the intersection point.

The angles that lie directly across from each other in this X are called vertical (or vertically opposite) angles.

  • They share the same vertex (corner point).
  • They are not next to each other (non‑adjacent).
  • Each intersection creates two pairs of vertical angles.

Think of the hands of a clock crossing: the opposite corners of the “X” made by the hands form vertical angles.

Key properties (quick facts)

  • Vertical angles are always congruent (have exactly the same measure).
  • The two angles in one pair of vertical angles form equal angles, no matter how the lines intersect.
  • All four angles around the intersection add up to 360°.
  • Adjacent angles (next to each other) formed by the same intersection are supplementary (they add to 180°), but they are not vertical angles.

Simple example

Imagine two lines intersecting so that one of the angles is 120°.

  • The angle directly opposite that 120° angle is also 120° (they are vertical angles and congruent).
  • The two angles next to the 120° angle are each 60°, and each 60° is vertical to the other 60°.

So the pairs of vertical angles here are:

  • 120° and 120°
  • 60° and 60°

Mini Q&A

  • Are vertical angles always equal?
    Yes, by the vertical angles theorem, vertical angles are always congruent.
  • Are vertical angles adjacent?
    No, they are opposite each other and do not share a side.
  • Can vertical angles be right angles?
    Yes, if the intersection forms 90° angles, then each pair of opposite 90° angles is a pair of vertical angles.

TL;DR: Vertical angles are the opposite angles formed when two lines cross, and each pair of vertical angles is always equal in measure.