Question

With the help of a compass, draw an angle equal in measure to each of the angles given below.

(3)

Answer 1

Let the given angle be named ∠ABC.
Steps of construction:
(1) Draw a ray EF.
(2) Place the point of compass at point B and cut two arcs of suitable radius, one on ray AB and the other on ray BC which intersects them at points P and Q, respectively.
(3) With the same radius, placing the point of compass at point E, draw an arc which intersects the ray EF at point G.
(4) Measure the arc PQ and with this radius, draw an arc with G as centre intersecting the previous arc at point H.
(5) Draw the ray HE.
(6) Take a point D on the ray HE.
Thus, ∠DEF is equal to ∠ABC.