Question

In $△$ NVY, ∠NVY = $\angle$VYN + $\angle$VNY. Which of the following is true?

• A. $△$NVY must be an isosceles triangle
• B. $△$NVY must be an acute angled triangle
• C. $△$NVY must be a right angled triangle
• D. Such a triangle can't be constructed

Answer 1

The correct option is C

$△$NVY must be a right angled triangle

In $△$ NVY,let us assume $\angle$VYN and $\angle$VNY be x and y. Third angle i.e.

$\angle$NVY = x + y
Applying angle sum property, (x + y) + x + y = ${180}^{\circ }$
2(x + y) = ${180}^{\circ }$
(x + y) = ${90}^{\circ }$
Since third angle is equal to ${90}^{\circ }$, it must be a right triangle