Mathematics

# In the given figure AB || CD; BC || DE then find the values of x and y.

##### SOLUTION
Given that $AB||CD$
Taking $BC$ as transversal,
$\angle ABC=\angle BCD$ (alternate interior angles)
$3x=105^{\circ}$
$x=35^{\circ}$
Also, given that $BC||DE$.
Taking $CD$ as transversal,
$\angle CDE=\angle BCD=105^{\circ}$ (alternate interior angles)
Now applying angle sum property in triangle $CDE$,
$\angle CDE+\angle DEC +\angle DCE=180^{\circ}$
$105^{\circ}+y+24^{\circ}=180^{\circ}$
$y=51^{\circ}$

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Subjective Medium Published on 09th 09, 2020
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