Mathematics
In the figure (i) given below, calculate the values of x and y.
Circles
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Answer
In the figure,
ABCD is a cyclic quadrilateral.
⇒ ∠B + ∠D = 180°
⇒ 40° + 45° + y = 180°
⇒ 85° + y = 180°
⇒ y = 180° - 85°
⇒ y = 95°.
Considering △ABD and △ACD,
∠ABD = ∠ACD = 40° (∵ angles in same segment are equal.)
x = 40°.
Hence, the value of x = 40° and y = 95°.
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