question_answer

In the given figure, show that CD II EF.

Answer:

\[\angle BAD=\angle BAE\text{ }+\angle EAD\]

\[=\text{ }40{}^\circ \text{ }+\text{ }30{}^\circ \]

\[=70{}^\circ \]

and \[\angle CDA\text{ }=\text{ }70{}^\circ \]

∴ \[\angle BAD=\angle CDA\]

But they form a pair of alternate angles.

AB||CD                      ...(i)

Also, \[\angle BAE+\angle AEF=40{}^\circ +140{}^\circ \]

\[=\text{ }180{}^\circ \]

But they form a pair of interior opposite angles.

AB||EF                        ...(ii)

From (i) and (ii), we get

AB||CD||EF

CD||EF

Total hours spend by Ritika for studies

= 11\[\frac{1}{3}\]hours = \[\frac{34}{3}\]hours