Question

Plz solve this question..Its urgent..​

Answer 1

Step-by-step explanation:

In circle with centre O, TN is tangent at E.

$\therefore OE \perp TN\\\\\therefore m\angle OET = m\angle OEN= 90\degree \\\\In\: \triangle OET\\\\\angle OET + \angle OTE +\angle TOE = 180°\\\\\therefore 90\degree + 35\degree+\angle TOE = 180°\\\\\therefore 125\degree+\angle TOE = 180\degree\\\\\therefore \angle TOE = 180\degree-125\degree\\\\\huge \red {\boxed{\therefore \angle TOE = 55\degree}} \\\\In\: \triangle OPE\\\\OP = OE... (radii\: of \:same \: circle) \\\\\therefore \angle OPE = \angle OEP..(1)\\ (\angle s \: opposite \: to \:equal\:sides) \\\\\angle TOE =\angle OPE +\angle OEP.. (2)\\(by\:exterior \:\angle\:theorem) \\\\\therefore 55\degree= \angle OPE +\angle OPE\\\{From\: equations\:(1) \&\:(2)\} \\\\\therefore 55\degree= 2\angle OPE \\\\\therefore \angle OPE = \frac{55\degree}{2}\\\\\huge \orange{\boxed{\therefore \angle OPE =27.5\degree}}$