Question

In the given figure, PA|| BC|| DT and AB|| DC. Then, the values of a and b are ______ respectively.

• A. ${60}^{\circ },{120}^{\circ }$
• B. ${50}^{\circ },{130}^{\circ }$
• C. ${70}^{\circ },{110}^{\circ }$
• D. ${80}^{\circ },{100}^{\circ }$

Answer 1

The correct option is B ${50}^{\circ },{130}^{\circ }$

It is given that, PA|| BC and AB is transversal,
$\therefore \angle PAB=\angle ABC$
[alternate interior angles]
$\Rightarrow {50}^{\circ }=a$
Also AB||DC and BC is transversal.
$\therefore \angle ABC+\angle DCB={180}^{\circ }$
[co-interior angles]
$\Rightarrow a+\angle DCB={180}^{\circ }\Rightarrow \angle DCB={180}^{\circ }-a\Rightarrow \angle DCB={180}^{\circ }-{50}^{\circ }$
[Using $a={50}^{\circ }$]
$\Rightarrow \angle DCB={130}^{\circ }$
Also BC|| DT and DC is transversal,
$\therefore \angle CDT=\angle DCB$
[alternate interior angles]
$\Rightarrow b={130}^{\circ }$