question_answer

In the adjoining figure/ p | | q. Find the unknown angles.

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,\[\angle a=55{}^\circ ,\angle b=125{}^\circ ,\angle c=55{}^\circ ,\angle d=125{}^\circ \]

\[\angle e=55{}^\circ \,and\,\angle f=55{}^\circ \].