Question

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

Answer 1

Answer:

Given an angle ABC with B as your center you should put the compass with center in B and make an arc with a length that is more than the double of the angle. There you have the intersections between the arc and the segments BA and BC lets say the intersections is D and E, you should open the compass from D to E and make an arc starting D which intersects the previous arc-lets say that intersection is F. Now you should draw a segment using the straight hedge which starts in B and passes through F and ends in a new point let's call that one G with a length similar to AB and BC. So now you have the angle ABG with the center as B which is adjacent and congruent to ABC.

Answer 2

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.

Mark an arc through the sides of the angle. Let the arc intersect the rays at A and B. Continue the arc on past B for a distance. 

Set the compass at B, and to the width of AB. 

Still with the compass at B, mark an arc to intersect the first arc at C. 

Now you have AB = BC. 

Since the radius OA=OB=OC, angles AOB and BOC are congruent.