In the figure, ABCD is a square. CDE is an equilateral triangle that lies inside the square, with E a point inside ABCD. Find ∠BAE.
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Worked Solution
Step 1: Square ABCD has all four interior angles equal to 90°, and all four sides equal. Equilateral triangle CDE has all three angles equal to 60° and all three sides equal to CD.
Step 2: Angle ADE = angle ADC − angle EDC = 90° − 60° = 30°.
Step 3: In triangle ADE, AD = DC (square side) and DE = DC (equilateral side), so AD = DE. Triangle ADE is isosceles.
Step 4: The two base angles of triangle ADE are equal: angle DAE = angle DEA = (180° − 30°) ÷ 2 = 75°.
Step 5: Angle BAE = angle BAD − angle DAE = 90° − 75° = 15°.
Correct answer: 15°
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