Q13 of 29 Page 61

In the figure at left ,ABCD is a cyclic quadrilateral in which AB || DC. If ∠BAD = 100°

find (i) ∠BCD (ii) ∠ADC (iii) ∠ABC.


As ABCD is a cyclic quadrilaterals, sum of all angles = 360°

As AB is parallel to CD


∠ADC = 180 – ∠DAB = 80° as they are interior angles on the same side.


As angle subtended by chord BD on circumference = 100°


Therefore ∠BCD = 100°


As ∠BCD and ∠ABC are interior angles


∠ABC = 180 – ∠BCD = 80°


More from this chapter

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11

In the figure at left, PQ is a diameter of a circle with centre O. If ∠PQR = 55°, ∠SPR = 25°and ∠PQM = 50°.

Find (i) ∠QPR, (ii) ∠QPM and (iii) ∠PRS.


 12

In the figure at right, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that ∠DBC = 30°and ∠BAC = 50°.

Find (i) ∠BCD (ii) ∠CAD


 14

In the figure at right, ABCD is a cyclic quadrilateral in which ∠BCD = 100°and ∠ABD = 50°. Find ∠ADB

 15

In the figure at left, O is the centre of the circle, ∠AOC = 100° and side AB is produced to D.

Find (i) ∠CBD (ii) ∠ABC