PLZZZZZZZZZZ HELP.....I HAVE MATHS EXAM TOMMOROW
ABCD is a cyclic quadrilateral whose diagonal intersects at a point E, if ∟DBC = 700 and ∟BAC= 300 , find ∟BCD, further if AB = BC find ∟ECD.
Answers
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°
It's ex 10.5 q 6 of class 9
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