In △NVY, if NV=VY and VY≠ YN, then which of the following is true?

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Question

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

Options:

A .

∠ N V Y

=

∠ V Y N

B .

∠ N V Y

=

∠ Y N V

C .

∠ N V Y

+

2 ∠ V Y N

=

180^{\circ}

D .

∠ V Y N

+

2 ∠ N V Y

=

180^{\circ}

Answer: Option C
:
C

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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