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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