 Vertical Angles

# Vertical angles

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Description:
In geometry, a pair of angles is said to be vertical (also opposite and vertically opposite, which is abbreviated as vert. opp. ∠s) if the angles are formed from two intersecting lines and the angles are not adjacent. They all share a vertex. Such angles are equal in measure and can be described as congruent.

## Vertical angle theorem

When two straight lines intersect at a point, four angles are made . The nonadjacent angles are called vertical or opposite or vertically opposite angles. Also, each pair of adjacent angles form a straight line and are supplementary. Since any pair of vertical angles are supplementary to either of the adjacent angles, the vertical angles are equal in measure.

## Algebraic solution for Vertical Angles

In the figure, assume the measure of Angle A = x. When two adjacent angles form a straight line, they are supplementary. Therefore, the measure of Angle C = 180 − x. Similarly, the measure of Angle D = 180 − x. Both Angle C and Angle D have measures equal to 180 - x and are congruent. Since Angle B is supplementary to both Angles C and D, either of these angle measures may be used to determine the measure of Angle B. Using the measure of either Angle C or Angle D we find the measure of Angle B = 180 - (180 - x) = 180 - 180 + x = x. Therefore, both Angle A and Angle B have measures equal to x and are equal in......

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