Using a protractor, draw an angle of measure 78°. With this angle as given, draw angles of measure 39° and 56°.

Given

Construct an angles 78°, 39° and 56°

Construct a ray OA.

Using protractor construct \$\angle AOB\$ of 78°

Taking O as centre and convenient radius, construct an arc which cut sides OA and OB at the point P and Q.

Taking P and Q as centres and radius which is more than half of PQ, construct two arcs which cuts each other at the point R.

Now join the points O and R and extend it to the point X.

Here, OR intersects the arc PQ at the point C.

Taking C and Q as centres and radius which is more than half of CQ, construct two arcs which cuts each other at point T.

Now join the points O and T and extend it to the point Y.

OX bisects ∠AOB It can be written as \$\angle AOX = ∠BOX = 78/2 = 39°\$

We know that

∠AOY = ∠AOX + ∠XOY = 39° + 17° = 56°

Here, ∠AOX is the required angle of 39° and ∠AOY is the required angle of 56°

Answer

\$\angle AOB\$ of 78° ,\$\angle AOX\$ of 39° and \$\angle AOY\$ = 56°