Question

Diagonals of a square IJKL intersects at point M, Find the measures of $\angle IMJ,\angle JIK\text{and}\angle LJK.$

Answer 1

Diagonals of a square are perpendicular bisectors of each other.
seg JL = seg IK
$\angle IMJ={90}^{\circ }$
$\angle JIL={90}^{\circ }\text{[Angle of a square]}$
Diagonals of a square bisect opposite angles.
$\angle JIK=\frac{90}{2}={45}^{\circ }$
$\angle IJK={90}^{\circ }\text{[Angle of a square]}$
$\angle LJK=\frac{90}{2}={45}^{\circ }$
Hence measures of $\angle IMJ,\angle JIK,\angle LJKare{90}^{\circ },{45}^{\circ }\text{and}{45}^{\circ }.$