Question

triangle XYZ is an isosceles right triangle, right angled at Y.M and N are mid points of XY and XZ respectively. find the measure of angle XNM.

Answer 1

If angleY=90°, angleX & Z=45° because XYZ is an isosceles triangle.
Niw, M and N are mid-points....
Therefore, MN=1/2(YZ) [By Mid point theorem]
angle M=90° [Mid point of XY which is 90°]
AngleX=45°
Therefore, angleZ=45°