PRACTICE PROBLEMS ON CYCLIC QUADRILATERAL WITH ANSWERS

Find the missing angles in the following problems given below.

Problem 1 :

Find x given : 

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

In Figure given below, PQRS is a cyclic quadrilateral whose diagonals intersect at A. If ∠SQR = 80° and ∠QPR = 30°, find ∠SRQ.

Solution

Problem 9 :

PQRS is a cyclic quadrilateral. If ∠Q = ∠R = 65°, find ∠P and ∠S.

Solution

Problem 10 :

In Figure given below, PQRS is a cyclic quadrilateral, and the side PS is extended to the point A. If ∠PQR = 80°, find ∠ASR.

Solution

Problem 11 :

Quadrilateral ABCD is inscribed in circle O, as shown below

If m∠A = 80°, m∠B = 75°, m∠C = (y + 30)°, and m∠D=(x − 10)°, which statement is true?

1) x = 85 and y = 50        2) x = 90 and y = 45

3) x = 110 and y = 75      4) x = 115 and y = 70

Solution

Problem 12 :

In the diagram below, quadrilateral ABCD is inscribed in circle P.

Solution

Problem 13 :

In the diagram below, quadrilateral ABCD is inscribed in circle O, m∠A = (2x)°, m∠B = (x − 10)°, and m∠C = (x + 15)°

What is m∠D?

1) 55°     2) 70°     3) 110°   4) 135°

Solution

Problem 14 :

In the accompanying diagram, quadrilateral ABCD is inscribed in circle O. If measure of arc AB = 132 and measure of arc BC = 82, find m∠ADC

Solution

Problem 15 :

Find the value of x in the given figure. 

Solution

Problem 16 :

In the given figure, AC is the diameter of the circle with center O. If <ADE = 30° ; <DAC = 35° and <CAB = 40°. Find (i) <ACD   (ii)  <ACB  (iii)  <DAE

Solution

Problem 17 :

Find all the angles of the given cyclic quadrilateral ABCD in the figure.

Solution

Problem 18 :

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that <DBC = 40° and <BAC = 60° find

(i)  <CAD   (ii)  BCD

Solution

Problem 19 :

Find the value of x if ABCD is a cyclic quadrilateral if ∠1 : ∠2 = 3 : 6.

a) 90°         b) 45°       c) 60°     d) 20°

Solution

Problem 20 :

ABCD is a cyclic parallelogram. Show that it is a rectangle.

Solution

Problem 21 :

If PQRS is a cyclic quadrilateral and PQ is diameter, find the value of ∠PQS.

a) 45°    b) 110°    c) 20°     d) 80°

Solution

Problem 22 :

Find the value of x and y if ABCD is cyclic quadrilateral.

a) 60°, 60°    b) 50°, 60°    c) 45°, 45°    d) 80°, 90

Solution

Problem 23 :

What is the value of ∠PQR if PQRS is cyclic quadrilateral and PS = SR?

a) 90°     b) 70°    c) 40°    d) 30°

Solution

Problem 24 :

What is the value of ∠PRQ if ∠PSR : ∠PQR = 1 : 2?

a) 50°     b) 10°    c) 90°     d) 45°

Solution

Problem 25 :

In the figure given below, 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

Solution

Problem 26 :

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

Solution

Problem 27 :

In the figure given below, O is the centre of a circle and <ADC = 120°. Find the value of x.

Solution

Problem 28 :

In the figure given below, ABCD is a cyclic quadrilateral in which AB || DC. If <BAD  =  100° find

(i) <BCD

(ii) <ADC

(iii) <ABC

Solution

Problem 29 :

In the figure given below, ABCD is a cyclic quadrilateral in which <BCD = 100° and <ABD = 50° find <ADB

Solution

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