Q3 of 100 Page 17

In Fig. 16.178, O is the centre of the circle. If ∠BOD=160°, find the values of x and y.

Given that,

O is the centre of the circle


We have,


∠BOD = 160o


By degree measure theorem,


∠BOD = 2 ∠BCD


160o = 2x


x = 80o


Therefore,


∠BAD + ∠BCD = 180o (Opposite angles of Cyclic quadrilateral)


y + x = 180o


y + 80o = 180o


y = 100o


More from this chapter

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1

In Fig. 16.176, Δ ABC is an equilateral triangle. Find m∠BEC.

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In Fig. 16.177, Δ PQR is an isosceles triangle with PQ=PR and m∠PQR=35°. Find m∠QSR and m∠QTR.

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In Fig. 16.179 ABCD is a cyclic quadrilateral. If ∠BCD=100° and ∠ABD=70°, find ∠ADB.

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If ABCD is a cyclic quadrilateral in which AD||BC (fig. 16.180). Prove that ∠B=∠C.