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Vertical Angles Theorem Calculator

Vertical and adjacent angles calculator. Given one angle, find its vertical and supplementary angles with relations—for middle school.

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Vertical angles are equal; adjacent angles sum to 180°
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Any angle formed by two intersecting lines, 0-180

📖 Tutorial | Vertical Angles

1. Definition
Two intersecting lines form four angles: opposite (non-adjacent) angles are vertical angles and are equal; adjacent angles are supplementary, summing to 180°.
2. Formula & Notation
aThe known angle
VerticalOpposite a, equals a
AdjacentNext to a, equals 180−a
3. Properties & Laws
  • Vertical angles are equal;
  • Adjacent angles are supplementary;
  • Two pairs of vertical angles;
  • All four sum to 360°.
4. Steps
  1. Enter the known angle a (0<a<180);
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: one angle is 50°.
Solution: vertical angle 50°, each adjacent angle 130°.
6. Common Pitfalls
Only vertical angles are equal; adjacent are supplementary;
Keep angle between 0 and 180;
Vertical angles require two intersecting lines.

❓ FAQ | Vertical Angles

What are vertical angles?
The opposite (non-adjacent) angles from two intersecting lines.
What property do they have?
Vertical angles are equal.
What do adjacent angles sum to?
Adjacent supplementary angles sum to 180°.
For 50°, what are the angles?
Vertical 50°, adjacent 130°.
Sum of all four angles?
360°.
Are vertical angles always equal?
Yes, it is their fundamental property.