Question

In the adjoining figure AB|| ED and EF || CD, then find the value of x.

• A. ${100}^o$
• B. ${90}^o$
• C. ${120}^o$
• D. ${110}^o$

Answer 1

Answer: (C)

${120}^o$

In given figure $AB\parallel ED$ and $EF\parallel CD$

$\angle DEF=90-\angle GEF=90-20={70}^0$

Given that $EF\parallel CD$ and line ED join these

$\therefore \angle DEF=\angle EDC={70}^0$

Join BD

$\angle CBD=90-\angle ABC=90-50={40}^0$

$\angle CDB=90-\angle CDE=90-70={20}^0$

In $\Delta BCD,$

$\angle CBD+\angle CDB+\angle BCD=180$

$40+20+x=180$

$\Rightarrow x=180-40-20={120}^0$