Find vertical (opposite) and adjacent angles from one known angle, or work out an elevation angle, rise or run from slope measurements.

Two intersecting straight lines make equal opposite angles and supplementary adjacent angles. Enter an angle strictly between 0° and 180°.

Result precision

Vertical Angle Formula

The following formula is used to calculate vertical angle pairs.

A=C , B=D

A = abs (b - 180)
  • Where A, B, C, and D are the vertical angles described in the diagram below.
vertical angles

Vertical Angle Definition

What are vertical angles? Vertical angles are two opposite angles created by intersecting lines. In the diagram above, A and C are vertical angles, and B and D are vertical angles. Vertical angles are always equal to one another. (A=C).

Example

How to calculate vertical angles?

  1. First, determine one given angle.

    In this example, angle A is given as 30 degrees.

  2. Using the formula above, determine the rest of the angles.

    Since C is equal to A, C = 30 degrees. B = abs (30-180) = 150. Since D is equal to B then D = 150. The final answer is A=30, C=30, B=150, D=150.

Vertical Angles

Are vertical angles congruent? By definition, vertical angles are considered congruent angles since the only requirement of congruent angles is that they are equal. This is the same as the definition for vertical angles.

Are vertical angles supplementary? A pair of vertical angles does not have to be supplementary, although they can be if they are equal to 90 degrees each.

Are vertical angles complementary? Vertical angles are only complementary when they are equal to 45 degrees. Adjacent linear-pair angles formed by intersecting straight lines sum to 180° and are supplementary.