Vertical Angles

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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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