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Question
In the given figure, if ABC is an equilateral triangle. Find ∠BDC and ∠BEC.
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Solution
It is given that, ABC is an equilateral triangle
We have to find `angleBDC` and `angleBEC`
Since ΔABC is an equilateral triangle
So, `angleA = angleB = angleC = 60°`
And ABEC is cyclic quadrilateral
So `angle A + angle E = 180°` (Sum of opposite pair of angles of a cyclic quadrilateral is 180°.)
Then,
`angle E = 180° - 60°`
= 120°
Similarly BECD is also cyclic quadrilateral
So,
`angle E + angle D = 180°`
`angleD = 180° - 120°`
= 60°
Hence, `angle BDC `= 60° and `angle BEC = 120°`.
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