Question

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

Step 1: Construct an arbitrary angle, with vertex at O using straightedge .

Step 2: Mark an arc through the sides of the angle using compass.

Step 3: Let the arc intersect the rays at A and B. Continue the arc on past B for a distance.

Step 4: Set the compass at B, and to the width of AB.

Step 5: Place the compass at B, mark an arc to intersect the first arc at C.

Now we get AB = BC.

Since the radius OA, OB and OC are equal.

Therefore,angles AOB and BOC are congruent.