Answer:
Given, p||q Here, \[\angle e+125{}^\circ =180{}^\circ \] [Linear pair] \[\angle e=180{}^\circ 125{}^\circ =55{}^\circ \] \[\angle f=\angle e=55{}^\circ \] [Vertically opposite angles] Since, p||q and t is a transversal. \[~\therefore \angle a=\angle f\] [Alternate angles] \[=55{}^\circ \] \[[\because \angle f=55{}^\circ ]\] \[\angle d=125{}^\circ \] [Corresponding angles] \[\angle c=\angle a=55{}^\circ \] [Vertically opposite angles] and \[\angle b=\angle d=125{}^\circ \] [Vertically opposite angles] Hence,\[\angle a=55{}^\circ ,\angle b=125{}^\circ ,\angle c=55{}^\circ ,\angle d=125{}^\circ \] \[\angle e=55{}^\circ \,and\,\angle f=55{}^\circ \].
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