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Diagonals of a square IJKL intersects at point M. Find the measures of ∠IMJ, ∠JIK and ∠LJK.

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i. IJKL is a square. [Given] 

∴ seg IK ⊥ seg JL [Diagonals of a square are perpendicular to each other]

∠ IMJ=90° 

∠ JIL 90° ……. (i) [Angle of a square] 

ii. ∠JIK = (1/2) ∠JIL [Diagonals of a square bisect the opposite angles] 

∠JIK = (1/2) (90°) [From (i) 

∴ ∠JIK = 45° 

∠IJK = 90° (ii) [Angle of a square] 

iii. ∠LJK = (1/2) ∠IJK [Diagonals of a square bisect the opposite angles] 

∠LJK = (1/2)(90°) [From (ii)] 

∴ ∠LJK = 45° 

∴ ∠LJK = 90°, ∠JIK = 45°, ∠LJK = 45°

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