Question

Find the value of $x$(in degrees), if $l||m$

Answer 1

Construct r such that

r|| l ||m

$\angle ABC=\angle BAP={70}^{\circ }\left(alternate\right)$

$⟹\angle BDN=180-150={30}^{\circ }$

($\because$sum of angles on a straight line=${180}^{\circ })$

$⟹\angle BDN=\angle DBC={180}^{\circ }\left(alternate\right)$

$⟹\angle ABD=\angle ABC+\angle DBC$

$=70+30=100-\left(1\right)$

$and\angle ABD={360}^{\circ }-(x-10)$

$=360-x+10$

$=370-x-\left(2\right)$

comparing 1& 2

$⟹100=370-x$

$⟹x={270}^{\circ }$