Question

In given figure, ABCD is a cyclic quadrilateral in which AF, EC, BE and BF are straight lines. If angle CBE =65^ and a= 2b/ 3 find values of a and b.​

Answer 1

$\underline\mathbb \pink{♥Ans:-}$

Sum of opposite angles of a cyclic quadrilateral = 180

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.

In cyclic quadrilateral ABCD:

⇒∠BAD+∠ADC=180

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⇒50

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+∠ADC=180

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⇒∠ADC=180

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⇒∠ADC+∠CDE=180

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(∵Sumofanglesonastraightline=180

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.)

⇒130

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+∠CDE=180

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⇒∠CDE=x=50

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Answer 2

Answer: For chord CD,

∠CBD=∠CAD      ...Angles in same segment

∠CAD=70°

∠BAD=∠BAC+∠CAD=30°+70°=100°

∠BCD+∠BAD=180°     ...Opposite angles of a cyclic quadrilateral

⇒∠BCD+100°=180°

⇒∠BCD=80°

In △ABC

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°

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