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Question
In the given figure, AC is the diameter of the circle with centre O. If ∠ADE = 30°, ∠DAC = 35° and ∠CAB = 40°. Find ∠DAE
Sum
Solution
In the cyclic quadrilateral ACDE,
∠AED = 180° – 55°
= 125°
In ΔAED,
∠DAE + ∠AED + ∠EDA = 180° ...(Sum of the angles of a triangle is 180°)
∠DAE + 125° + 30° = 180°
∠DAE = 180° − 155°
= 25°
∴ ∠DAE = 25°
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Exterior Angle of a Cyclic Quadrilateral
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Chapter 4: Geometry - Exercise 4.4 [Page 173]
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