Question

What is the 4th step in the construction of $\angle PQR$, which is equal in measure to $\angle ABC$ ?
1)Draw ray QR.
2) Place the compass point at vertex B of ∠ABC
and taking a convenient distance, draw an arc
to cut the rays BA and BC at points D and E
respectively.

3) Using the same distance again, place the
compass point at point Q of ray QR and draw
an arc. Let this arc cut the ray QR at T.

• A. Now place the compass point on point T.
• B. Draw the ray QS. Take any point P on ray QS.
• C. Now, place the point of the compass at point E and open the compass to a distance equal to DE.
• D. Using a protractor verify that the ∠PQR so formed is of
  the same measure as ∠ABC.

Answer 1

The correct option is C Now, place the point of the compass at point E and open the compass to a distance equal to DE.

To construct $\angle PQR$ equal in measure to $\angle ABC$, using a compass and a ruler, the order of steps are:
1)Draw ray QR.
2) Place the compass point at vertex B of ∠ABC
and taking a convenient distance, draw an arc
to cut the rays BA and BC at points D and E
respectively.

3) Using the same distance again, place the
compass point at point Q of ray QR and draw
an arc. Let this arc cut the ray QR at T.
4) Now, place the point of the compass at point E and open the compass to a distance equal to DE.
5) Now place the compass point on point T.
6) Using the distance equal to DE, draw an arc to cut the previous arc at S.
7)Draw the ray QS. Take any point P on ray QS.
8) Using a protractor verify that the ∠PQR so formed is of
the same measure as ∠ABC.