In the given diagram, equilateral triangle EAB surmounts square ABCD. Find the the measure of ∠AEC.
A
30∘
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B
15∘
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C
45∘
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D
25∘
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Solution
The correct option is C45∘ In △BCE ∠BCE+∠BEC+∠CBE=180∘ [BE=BC⟹∠BCE=∠BEC]
And,
Since △EAB is equilateral and ABCD is square, ∠CBE=90∘+60∘=150∘ ⟹2∠BEC+150∘=180∘⟹∠BEC=15∘
Since △EAB is equilateral, ∠AEB=60∘⟹∠AEC+∠BEC=60∘⟹∠AEC=60∘−15∘=45∘