prove that vertically opposite are angles
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Vertical Angles: Theorem and Proof
Theorem: In a pair of intersecting lines the vertically opposite angles are equal. It can be seen that ray \overline{OA} stands on the line \overleftrightarrow{CD} and according to Linear Pair Axiom, if a ray stands on a line, then the adjacent angles form a linear pair of angles.
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A pair of vertically opposite angles are always equal to each other. ... For example, if two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°. And the angle adjacent to angle X will be equal to 180 – 45 = 135°.
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