  A mobile agent equipped with a compass and a measure of length has to find an
inert treasure in the Euclidean plane. Both the agent and the treasure are
modeled as points. In the beginning, the agent is at a distance at most $D>0$
from the treasure, but knows neither the distance nor any bound on it. Finding
the treasure means getting at distance at most 1 from it. The agent makes a
series of moves. Each of them consists in moving straight in a chosen direction
at a chosen distance. In the beginning and after each move the agent gets a
hint consisting of a positive angle smaller than $2\pi$ whose vertex is at the
current position of the agent and within which the treasure is contained. We
investigate the problem of how these hints permit the agent to lower the cost
of finding the treasure, using a deterministic algorithm, where the cost is the
worst-case total length of the agent's trajectory. It is well known that
without any hint the optimal (worst case) cost is $\Theta(D^2)$. We show that
if all angles given as hints are at most $\pi$, then the cost can be lowered to
$O(D)$, which is optimal. If all angles are at most $\beta$, where $\beta<2\pi$
is a constant unknown to the agent, then the cost is at most
$O(D^{2-\epsilon})$, for some $\epsilon>0$. For both these positive results we
present deterministic algorithms achieving the above costs. Finally, if angles
given as hints can be arbitrary, smaller than $2\pi$, then we show that cost
$\Theta(D^2)$ cannot be beaten.
