wiz-icon
MyQuestionIcon
MyQuestionIcon
2011
You visited us 2011 times! Enjoying our articles? Unlock Full Access!
Question

Prove that, the sum of either pair of opposite angles of a cyclic quadrilateral is 180.

Open in App
Solution

Given : ABCD is a cyclic quadrilateral of a circle with centre at O.
To prove : BAD+BCD=180o
ABC+ADC=180o
Chord AB
5=8.....(1) [Angle in same segment are equal]

Chord BC
1=6.....(2) [Angle in same segment are equal]

Chord CD
2=4.....(3) [Angle in same segment are equal]

Chord AD
7=3.....(4) [Angle in same segment are equal]

By angle sum property of qudrilateral
A+B+C+D=360o

1+2+3+4+7+8+5+6=360o

(1+2+7+8)+(3+4+5+6)=360o

(1+2+7+8)+(7+2+8+1)=360o [From (1), (2) ,(3) and (4)]

2(1+2+7+8)=360o

1+2+7+8=180o

(1+2)+(7+8)=180o

BAD+BCD=180o

Similarly,
ABC+ADC=180o

Hence proved.

1106596_1203832_ans_4ffc807d26354e3b9b6a3d0a8017bd0c.png

flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Quadrilaterals
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon