Question

Question 101

In the given figure, if l || m, find the values of a and b.

Answer 1

since l, m are parallel lines and t is transversal.

$\therefore \angle EAB+\angle DBA={180}^{\circ }\left[consecutiveinteriorangles\right]\Rightarrow b+{132}^{\circ }={180}^{\circ }\Rightarrow b={180}^{\circ }-{132}^{\circ }\Rightarrow b={48}^{\circ }$
Again, l, m are parallel lines and s is transversal.
$Therefore,\angle EAC+\angle BCA={180}^{\circ }\left[consecutiveinteriorangles\right]\Rightarrow a+b+{65}^{\circ }={180}^{\circ }\Rightarrow a+{48}^{\circ }+{65}^{\circ }={180}^{\circ }\Rightarrow a={180}^{\circ }-{48}^{\circ }-{65}^{\circ }[\therefore b={48}^{\circ }]\Rightarrow a={67}^{\circ }$