Question

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

Answer 1

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 $CDE$,

$\angle CDE+\angle DEC+\angle DCE={180}^{\circ }$

${105}^{\circ }+y+{24}^{\circ }={180}^{\circ }$

$y={51}^{\circ }$