Question

Question 17

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

(a) ${60}^{\circ },{120}^{\circ }$
(b) ${50}^{\circ },{130}^{\circ }$
(c) ${70}^{\circ },{110}^{\circ }$
(d) ${80}^{\circ },{100}^{\circ }$

Answer 1

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