In cyclic quadrilateral ABCD, diagonals AC and BD intersect
at P. If Z DBC = 70° and Z BAC = 30°, then find BCD.
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hey mate/////
here is ur answer
The region between a chord and either of its arcs is called a segment the circle.
Angles in the same segment of a circle are equal.
For chord CD,
We know, that Angles in same segment are equal.
∠CBD = ∠CAD
∠CAD = 70°
∠BAD = ∠BAC + ∠CAD = 30° + 70° = 100°
∠BCD+∠BAD= 180°
(Opposite angles of a cyclic quadrilateral)
∠BCD + 100° = 180°
∠BCD = 180° - 100°
∠BCD =80°
In ΔABC
AB = BC (given)
∠BCA = ∠CAB (Angles opposite to equal sides of a triangle)
∠BCA = 30°
also, ∠BCD = 80°
∠BCA + ∠ACD = 80°
30° + ∠ACD = 80°
∠ACD = 50°
∠ECD = 50°
Hence, ∠BCD = 80° & ∠ECD = 50°
#answerwithquality and #BAL
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