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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