Question

in the given figure, ABCD is a cyclic quadrilateral. If ∠BCX=70° and ∠ADX'=80°, then find x and y.

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Answer 1

ANSWER:

Given,  ∠BCX=70° and ∠ADX'=80°

To Find: x and y

Solution:  ∵ ∠ADX' and ∠ADC are linear pair.

∴∠ADX' + ∠ADC = 180°

⇒∠ADC = 180° - 80°

⇒∠ADC = 100°

Now, ∠ADC + ∠ABC = 180° [Sum of any two opposite angles of a cyclic quadrilateral is 180°]

⇒100° + y = 180°

⇒y = 180° - 100°

⇒y = 80°

Again, ∠BCX + ∠BCD = 180° [Linear Pair]

⇒∠BCD = 180° - 70°

⇒∠BCD = 110°

Also, ∠BCD + ∠ABD = 180° [Sum of any two opposite sides of a cyclic quadrilateral is 180°]

⇒110° + x = 180°

⇒x = 180° - 110°

⇒x = 70°

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