Question

Given that $AB\parallel DE$, $\angle ABC={115}^o$, $\angle EDC={140}^o$, then the value of $x$ is:

• A. ${45}^o$
• B. ${55}^o$
• C. ${65}^o$
• D. ${75}^o$

Answer 1

The correct option is D ${75}^o$

Extend the lines $AB$ and $DE$ to $G$ and $F$ respectively.

then, $\angle ABO=\angle DOB=115°$

So, $\angle DOC=180°-115°$

$=65°$

$\angle ODC=180°-140°=40°$

Consider $△ODC,$ $65°-40°+\angle OCD=180°$

$⟹x=75°$