Question

In ∆ABC, line segment DE is parallel to BC. Find x,y and z.

please can you solve it.​

Answer 1

$\huge\mathbb{\underline{QUESTION:-}}$

In ∆ABC, line segment DE is parallel to BC. Find x,y and z.

$\huge\mathbb{\underline{\blue{SOLUTION:-}}}$

$\huge\boxed{\underline{\red{\bold{Given :-}}}}$

DE||BC

we have to find the value of x ,y ,and z

$\sf\large\underline{\underline{\red{According\: to\: question:-}}}$

DE||BC

So $\sf\angle ADE=\angle DBC$

(Corresponding angle)

$\sf \implies z=70^{\circ}$

(corresponding angle )

$\sf \angle AED= \angle ECD$

(corresponding angle)

$\sf\implies y=50^{\circ}$

(corresponding )

To find the value of z

we know that the sum of angels of triangle=$\sf 180^{\circ}$

$\sf\underline{\underline{\red{Now :-}}}$

$\sf \angle A+ \angle B+\angle C=180^{\circ}$

We find :-

$\sf \angle A=?\\ \sf \angle B=70^{\circ}\\ \sf\angle C=50^{\circ}$

$\sf\longrightarrow \angle A+50^{\circ} + 70^{\circ}=180^{\circ}\\ \sf\longrightarrow \angle A +120^{\circ}=180^{\circ}\\ \sf\longrightarrow \angle A=180^{\circ}-120^{\circ}\\ \sf\longrightarrow \angle A=60^{\circ}$

$\sf\implies x=\angle A$

$\large\boxed{\sf{x=60^{\circ},y=50^{\circ},z=70^{\circ}}}$.