Question
Download Solution PDFIn the figure given below, ABCD is a square and DEC is an equilateral triangle. The points A and E are joined by a straight line.
Then, ∠DAE equals
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 1.
Given: ABCD is a square and DEC is an equilateral triangle. Points A and E are joined by a straight line.
Calculation:
⇒ ABCD is a square, then ∠ADC = 90°
AB=BC=CD=DA
⇒ DCE is an equilateral triangle, then ∠EDC = 60°
DC=DC=CE
⇒ Hence, AB=BC=CD=DA=CE=DC
⇒ Now, In △ADE,
AD=DE
⇒ If two sides are equal , then the two angles opposite to the equal sides will also be equal.
⇒ Thus, ∠AED=∠DAE=x°
∠ADE=∠ADC+∠EDC
∠ADE=90°+60°
∠ADE=150°
Sum of angles of triangle ADE = 180
∠ADE+∠AED+∠DAE=180
150+x+x=180
⇒ x=15°
Hence, ∠DAE=15°
Last updated on Jun 26, 2025
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