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,
$\therefore \angle PAB=\angle ABC\left[alternateinteriorangles\right]\Rightarrow {50}^{\circ }=a$
Also AB||DC and BC is transversal.
$\therefore \angle ABC+\angle DCB={180}^{\circ }\left[consecutiveinteriorangles\right]\Rightarrow a+\angle DCB={180}^{\circ }\Rightarrow \angle DCB={180}^{\circ }-a\Rightarrow \angle DCB={180}^{\circ }-{50}^{\circ }[Usinga={50}^{\circ }]\Rightarrow \angle DCB={130}^{\circ }$
Also BC|| DT and DC is transversal,
$\therefore \angle CDT=\angle DCB\left[alternateinteriorangles\right]\Rightarrow b={130}^{\circ }$