# Math

Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.

I think the answer is that you use the straightedge to draw two parallel lines and then you draw a line that goes through them that is perpendicular. You then use the compass to measure the angles, they should be congruent and adjacent. Any help would be appreciated.

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1. Construct the angle, with vertex at O

Draw a circle with center at O so it intersects the sides of the angle at A and B. (Extend the sides if necessary)

Place the compass on B and draw a circle of radius BA.

Circle B intersects circle O at C.

Since the arcs BA and CB are equal, so are the angles BOA and BOC. The angles are adjacent and congruent.

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