Question

Triangle XYZ is an isosceles right triangle ,right angled atY. M and N are midpoints of XY and XZ respectively find the measure of angle XNM

• A. undefined
• B. undefined
• C. undefined
• D. undefined

Answer 1

$\Delta XYZ$ is an isosceles right triangle.
$\Rightarrow \angle X=\angle z=\frac{1}{2}\times {90}^{\circ }={45}^{\circ }...\left(i\right)$
In $\Delta XYZ$, M and N are the mid-points of XY and XZ respectively.
$\therefore MN||YZ$ .....[Mid -point theorem]
$\therefore \angle XNM=\angle XZY$ ....[Corresponding angles]
$\therefore \angle XNM={45}^{\circ }$ ....[From (i)]