Question

In the figure shown $AB$ is parallel to $DE$. The difference between angles $xandy$ is

• A. $0^{\circ }$
• B. $4^{\circ }$
• C. ${10}^{\circ }$
• D. ${12}^{\circ }$

Answer 1

The correct option is B $4^{\circ }$

$SinceAB\parallel DE\angle AED=\angle BAE\left[Alternateinteriorangles\right]\angle BAE=35\Rightarrow \angle AED=\mathrm{35..}\left(1\right)In△CDE\angle CDE+\angle DEC+\angle DCE=180\left(AnglesumProperty\right)\angle CDE=53\left(Given\right)\angle DEC=\angle AED=35\angle DCE=x\Rightarrow 53+35+x=180\Rightarrow x=180-88=92x+y=180\left(LinearPairofangles\right)\Rightarrow y=180-x\Rightarrow y=180-92=88Hencex-y=92-88=4Sinceoption\left(B\right)istherightanswer$