A- - NVY - V Y NB- - NV Y - Y NVC- - NV Y -2 - V Y N -180-D- - V Y N -2 - N V Y -180-

The correct option is C ∠ NVY+ nbsp;2∠ VYN = 180^∘ Given, in NVY, NV = VY. Then, ∠ VYN nbsp;= ∠ YNV. nbsp; [angles opposite to equal sides of a trian ...

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Byju's Answer

Standard IX

Mathematics

Triangles

A. ∠ NVY =∠ V...

Question

In $△ N V Y$ , if $N V = V Y$ and $V Y \neq Y N$ , then which of the following is true?

$∠ N V Y$ = $∠ V Y N$

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$∠ N V Y$ = $∠ Y N V$

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$∠ N V Y$ + $2 ∠ V Y N$ = $180^{\circ}$

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$∠ V Y N$ + $2 ∠ N V Y$ = $180^{\circ}$

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Solution

The correct option is C
$∠ N V Y$ + $2 ∠ V Y N$ = $180^{\circ}$

Given, in $△ N V Y$ , NV = VY.

Then, $∠ V Y N = ∠ Y N V$ .
[angles opposite to equal sides of a triangle are equal]
Using angle sum property of a triangle, we get:
$∠ N V Y + ∠ V Y N + ∠ Y N V = 180^{\circ}$
So, $∠ N V Y + 2 ∠ V Y N = 180^{\circ}$ .

It is also given that $V Y \neq Y N$ . Hence the options $∠ N V Y = ∠ V Y N$ and $∠ N V Y = ∠ Y N V$ are not correct.

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