Here is the answer to your query.
Here are the steps to construct an angle of measure 15°.
Step 1 : Draw a ray OA. Now taking O as centre and convenient radius draw an arc intersecting OA at B.
Step 2: Taking B as centre and with the same radius before draw an arc intersecting the previously drawn arc at C.
Step 3 : Taking B and C as centre, draw arcs of same radius to intersect each other at D.
Now ∠AOD = 30°. Let BC intersect OD at E.
Step 4: Taking E and B as centre, draw arcs of same radius to intersect each other at F. Join OF.
Thus ∠AOF = 15°.