Question

in the given figure ,show that XY||EF .​

Answer 1

Step-by-step explanation:

xyb = ybs

by alternate angle test

ef ll xy

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Answer 2

$\huge\underline\mathfrak{Answer:}$

We have

$\angle$YRS = $\angle$YRE + $\angle$ERS

$\implies$$\angle$YRS = 36° + 30°

$\implies$$\angle$YRS = 66°

$\therefore$$\angle$XYR = $\angle$YRS

Thus, lines XY and RS are intersected by the line YR such that $\angle$XYR = $\angle$YRS, i.e., the alternate angles are equal.

• $\therefore$ XY ll RS..... 1.

Now, $\angle$ERS + $\angle$REF = 30° + 150°

= 180°.

This shows that the sum of interior angles on the same side of the TRANSVERSAL RE is 180°, i.e, they are supplementary.

• $\therefore$RS ll EF ..... 2.

From (1) and (2)

XY ll RS and RS ll EF

$\implies$ XY ll EF

Hence, XY ll EF.