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Question
Diagonals of a square IJKL intersects at point M, Find the measures of ∠IMJ, ∠JIK and ∠LJK .
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Solution
`square` 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]
∠JIK = `1/2` ∠JIL ...[Diagonals of a square bisect the opposite angles]
∠JIK = `1/2 xx 90°` ...[From (i)]
∴ ∠JIK = 45°
∠IJK = 90° ...(ii) ...[Angle of a square]
∠LJK = `1/2` ∠IJK ...[Diagonals of a square bisect the opposite angles]
∠LJK = `1/2xx 90°` ...[From (ii)]
∴ ∠LJK = 45°
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