Question

If $AB\parallel CD,EF\parallel GH$, then which of the following is true for measure of $\angle a,\angle b,\angle c$ ?

• A. ${114}^{\circ },{46}^{\circ },{114}^{\circ }$
• B. ${44}^{\circ },{116}^{\circ },{114}^{\circ }$
• C. ${112}^{\circ },{46}^{\circ },{44}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${114}^{\circ },{46}^{\circ },{114}^{\circ }$

Given:

$AB\parallel CD\Rightarrow e={134}^{\circ }$(corresponding angles are equal)

$\Rightarrow b+e={180}^{\circ }$.......$\left(linearpair\right)$

$\Rightarrow {134}^{\circ }+b={180}^{\circ }$

$\Rightarrow b={180}^{\circ }-{134}^{\circ }={46}^{\circ }$

Now,$f={66}^{\circ }$(vertically opposite angles are equal)

$\Rightarrow a+f={180}^{\circ }$(sum of co-interior angles $={180}^{\circ },consideringEF\left|\right|GH$)

$\Rightarrow a+{66}^{\circ }={180}^{\circ }$

$\Rightarrow a={180}^{\circ }-{66}^{\circ }={114}^{\circ }$

Also,$g={66}^{\circ }$,$\left(correspondinganglesareequal\right)$ considering $AB\left|\right|CD$ and $GH$ as transversal

$\Rightarrow c+g={180}^{\circ }$(linear pair)

$\Rightarrow c+{66}^{\circ }={180}^{\circ }$

$\Rightarrow c={180}^{\circ }-{66}^{\circ }={114}^{\circ }$

$\therefore a={114}^{\circ },b={46}^{\circ },c={114}^{\circ }$