Q6 of 100 Page 17

In Fig. 16.181, O is the centre of the circle. Find ∠CBD.

Given that,

∠BOC = 100o


By degree measure theorem,


∠AOC = 2 ∠APC


100o = 2 ∠APC


∠APC = 50o


Therefore,


∠APC + ∠ABC = 180o (Opposite angles of a cyclic quadrilateral)


50o + ∠ABC = 180o


∠ABC = 130o


Therefore,


∠ABC + ∠CBD = 180o (Linear pair)


130o + ∠CBD = 180o


∠CBD = 50o


More from this chapter

All 100 →
4

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

 5

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

 7

In Fig. 16.182, AB and CD are diameters of a circle with centre O. If ∠OBD=50°, find ∠AOC.

 8

On a semi-circle with AB as diameter, a point C is taken, so that m(∠CAB)= 30°. Find m(∠ACB) and m(∠ABC).