Question

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

• A. $\angle NVY$ = $\angle VYN$
• B. $\angle NVY$ = $\angle YNV$
• C. $\angle NVY$+ $2\angle VYN$ = ${180}^{\circ }$
• D. $\angle VYN$ + $2\angle NVY$ = ${180}^{\circ }$

Answer 1

The correct option is C

$\angle NVY$+ $2\angle VYN$ = ${180}^{\circ }$

Given, in $△NVY$, NV = VY.


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

It is also given that $VY\ne YN$. Hence the options $\angle NVY=\angle VYN$ and $\angle NVY=\angle YNV$ are not correct.