Question

In the figuere, if $AE||DCandAB=AC,\text{the value of}\angle ABDis$

• A. ${70}^{\circ }$
• B. ${110}^{\circ }$
• C. ${120}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is B

${110}^{\circ }$

(b),

In the figure, $AE||DC$

$\therefore \angle 1={70}^{\circ }\text{(Vertically opposite angles)}$

$\therefore \angle 1=\angle 2\text{(Alternate angles)}$

$\angle 2=\angle ABC$

(Base angles of isosceles triangle)

$\therefore \angle ABC={70}^{\circ }$

$But\angle ABC+\angle ABD={180}^{\circ }\text{(Linear pair)}$

$\Rightarrow {70}^{\circ }+\angle ABD={180}^{\circ }$

$\Rightarrow \angle ABD={180}^{\circ }-{70}^{\circ }={110}^{\circ }$

$\therefore \angle ABD={110}^{\circ }$