wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

ABCD is a cyclic quadrilateral. Then which of the angles given add to 180?


A

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 3

In a cyclic quadrilateral sum of opposite internal angles is 180

Therefore, opposite internal angles in a cyclic quadrilateral are supplementary.

Let O be the centre of the circle that can pass through ABCD. AC is the chord of the circle.

Join AC and BD
Since sum of all the angles in a triangle is 180,
We have thatCAB + ABC+ACB = 180
Also angles in a same segment are equal we have thatCAB = BDC and also ACB = ADB
Adding both the equations we get BDC + ADB = CAB + ACB
If we addABC on both sides, we get thatABC + BAC + ACB = ABC + ADC.
As ABC,BAC,ACB are angles in a triangle, their sum will be 180
Therefore ABC + ADC = 180
Similarly, we can prove that other pairs of internal opposite angles are supplementary.
Thus, BAD + BCD = 180


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circles and Quadrilaterals - Theorem 11
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon