Mathematics
Calculate the angles x, y and z if :
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Circles
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Answer
Let = k.
∴ x = 3k, y = 4k and z = 5k.
From figure,
∠BCP = ∠DCQ [Vertically opposite angles are equal.]
Exterior angle of a triangle is equal to the sum of two opposite interior angles.
∠ABC = ∠BCP + ∠BPC = x + y = 3k + 4k = 7k
∠ADC = ∠DCQ + ∠DQC = x + z = 3k + 5k = 8k.
ABCD is a cyclic quadrilateral.
We know that,
⇒ ∠ABC + ∠ADC = 180° [Sum of opposite angles in a cyclic quadrilateral = 180°]
⇒ 8k + 7k = 180°
⇒ 15k = 180°
⇒ k = = 12°.
x = 3k = 3 x 12° = 36°
y = 4k = 4 x 12° = 48°
z = 5k = 5 x 12° = 60°.
Hence, x = 36°, y = 48° and z = 60°.
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