Question

In the given figure AB is parallel to ED. If $\angle ABC={50}^{\circ }$ and $\angle EDC={40}^{\circ }$

then find the value of a and b.

• A. $a={90}^{\circ }andb={270}^{\circ }$
• B. $a={290}^{\circ }andb={70}^{\circ }$
• C. $a={270}^{\circ }andb={90}^{\circ }$
• D. $a={250}^{\circ }andb={110}^{\circ }$

Answer 1

The correct option is C

$a={270}^{\circ }andb={90}^{\circ }$

Construction: Draw a line FG through C such that $FG\parallel AB\parallel ED$ as shown.

$\Rightarrow \angle ABC=\angle BCF={50}^{\circ }\left(Alternateangles\right)$

$\Rightarrow \angle BCF={20}^{\circ }$

$\Rightarrow \angle FCD=\angle CDE={40}^{\circ }\left(Alternateangles\right)$

$\Rightarrow \angle FCD={40}^{\circ }$

$b=\angle BCF+\angle FCD$

$b={50}^{\circ }+{40}^{\circ }={90}^{\circ }$

$a={360}^{\circ }-b\left(Angleaboutapoint\right)$

$a={360}^{\circ }-{90}^{\circ }={270}^{\circ }$