In the given figure, △ ABC is equilateral. Find(i) ∠BDC,(ii) ∠BE

1.	In the given figure, △ ABC is equilateral. Find(i) ∠BDC,(ii) ∠BEC.
Answer» It is given that △ ABC is equilateral We know that ∠BAC = ∠ABC = ∠ACB = 60^o (i) We know that the angles in the same segment of a circle are equal ∠BDC = ∠BAC = 60^o So we get ∠BDC = 60^o (ii) We know that the opposite angles of a cyclic quadrilateral are supplementary So we get ∠BAC + ∠BEC = 180^o By substituting the values 60^o + ∠BEC = 180^o On further calculation ∠BEC = 180^o – 60^o By subtraction ∠BEC = 120^o

In the given figure, △ ABC is equilateral. Find(i) ∠BDC,(ii) ∠BEC.

Answer»

It is given that △ ABC is equilateral

We know that

∠BAC = ∠ABC = ∠ACB = 60^o

(i) We know that the angles in the same segment of a circle are equal

∠BDC = ∠BAC = 60^o

So we get

∠BDC = 60^o

(ii) We know that the opposite angles of a cyclic quadrilateral are supplementary

So we get

∠BAC + ∠BEC = 180^o

By substituting the values

60^o + ∠BEC = 180^o

On further calculation

∠BEC = 180^o – 60^o

By subtraction

∠BEC = 120^o

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In the given figure, △ ABC is equilateral. Find(i) ∠BDC,(ii) ∠BEC.

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