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In figure (1) given below, equilateral triangle EBC surmounts square square ABCD. Find angle BED represented by x.

In figure (1) given below, equilateral triangle EBC surmounts square square ABCD. Find angle BED represented by x. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Rectilinear Figures

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Answer

△EBC is an equilateral triangle, so all sides are equal.

EB = BC = EC ……..(i)

In square all sides are equal

AD = CD = BC = AB ……..(ii)

From (i) and (ii) we get,

BC = EC = CD

⇒ EC = CD.

In △ECD,

EC = CD

⇒ ∠DEC = ∠CDE = a (let) (Angles opposite to equal sides are equal in isosceles triangle)

⇒ ∠C = ∠ECB + ∠BCD

∠ECB = 60° (As each angle of a equilateral triangle = 60°)

∠BCD = 90° (As each angle of a square = 90°)

⇒ ∠C = 60° + 90° = 150°.

⇒ ∠DEC + ∠CDE + ∠C = 180

⇒ a + a + 150° = 180°

⇒ 2a = 180° - 150°

⇒ 2a = 30°

⇒ a = 15°.

From figure,

x° = ∠BEC - ∠DEC = 60° - 15° = 45°.

Hence, x = 45.

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