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

Answer 1

If you have angle AOB and want to construct BOC such that AOB and BOC are congruent,

with the compass draw an arc subtended by AOB and extending beyond OB. Let the arc intersect OA at D and OB at E.

Place the compass at E and set to the distance ED. Then draw a circle with radius ED which intersects the extended arc DE at C.

angle BOC is congruent to AOB because it subtends an equal arc and has the same radius