Question

c.In the following figure, BD=DC and CBD=30°, find ZBAC
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Answer 1

answer:-- It is given that BD = DC

From the figure we know that

∠BCD = ∠CBD = 30o\°

Consider △ BCD

Using the angle sum property

∠BCD + ∠CBD + ∠CDB = 180°

By substituting the values

30o° + 30° + ∠CDB = 180o

On further calculation

∠CDB = 180° – 30° – 30°

By subtraction

∠CDB = 180° – 60°

So we get

∠CDB = 120°

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

It can be written as

∠CDB + ∠BAC = 180o

By substituting the values

120° + ∠BAC = 180°

On further calculation

∠BAC = 180o° – 120°

By subtraction

∠BAC = 60°

Therefore, ∠BAC = 60°

hope it helps you ❤️...