Step-by-step explanation:
In circle with centre O, TN is tangent at E.
[tex] \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}} [/tex]
