Question

in the given figure 'o' is the centre of the circle. XY is a tangent.
if PQY =55° then OPQ = ?
please answer this accurately​

Answer 1

Answer:

∠OPQ=35°

Step-by-step explanation:

As we know tangent is always perpendicular to the radius of the circle.

Thus, ∠OQY=90°

But, ∠PQY=55°...(Given)

Thus,

∠OQY=90°-55°

∠OQY=35°....(1)

Now,

In ΔOPQ,

OQ=OP ....(Radii of same circle)

Thus,

ΔOPQ is an isosceles triangle.

Therefore,

∠OQP=∠OPQ

From (1),

Therefore, ∠OPQ=35°