Question

In the figure ( not drawn to scale), $ABCD$ is a trapezium with $AB$ parallel to $DC$, $AC$ $=$ $AD$ and $EAC$ is a straight line. Find $y$.

• A. ${56}^o$
• B. ${41}^o$
• C. ${75}^o$
• D. ${98}^o$

Answer 1

Answer: (C)

${75}^o$

Since $AD=AC$

$\Rightarrow \angle ADC=\angle ACD=x$

$x+x={82}^{\circ }$ exterior angle property

$\Rightarrow x={41}^{\circ }$

Now $AB$ & $D$C are parallel.

$\Rightarrow \angle ABC+\angle BCD={180}^{\circ }$ .....Co-interior angles of two parallel lines.

$\Rightarrow y+({64}^{\circ }+x)={180}^{\circ }$

$\Rightarrow y+\left({105}^{\circ }\right)={180}^{\circ }$

$\Rightarrow y={75}^{\circ }$