I have drawn an isosceles triangle ABC whose included angle of two equal sides is ∠ABC=45°; the bisector of ∠ABC intersects the side AC at the point D let us determine the circular values of ∠ABD, ∠BAD, ∠CBD and ∠BCD.

∠ABC = 45°
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∵ BD is the angle bisector of ∠ABC
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∠BAD + ∠ABC+ ∠BCD = π
∵ ABC is an isosceles triangle
⇒ ∠BAD = ∠BCD = x
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