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ICSE Class 9 Answered

In the adjoining figure, equilateral 🔺EDC Surmounts square ABCD.if angle DEB=x degrees,find the value of x
Asked by naikraju023 | 11 Jun, 2019, 01:04: PM
Expert Answer
ABCD is a square.
angle DCB = 90°
ΔEDC is equilateral hence, angle ECD = 60°
angle ECB = angle ECD + angle DCB
               = 90° + 60° = 150°
EC = CB
angle CEB = angle CBE = y    angle opposite to equal sides
In ΔECB,
angle ECB + angle CEB + angle CBE = 180°
150° + y + y = 180°
2y = 30°
y = 15°
angle DEC = 60°
x + 15° = 60°
x = 45°
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