Angle Subtended by an Arc of a Circle on the Circle and at the Center
Match the unk...
Question
Match the unknown angle x in each case if O is the centre of each circle.
A
40∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
30∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
90∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
Since the angle subtended by an arc at the centre of a circle is double the angle subtended by it on any remaining part of the circle, x=∠AEB=12∠AOB=12×80∘=40∘
x=∠ACB=12∠AOB=12×60∘=30∘
it can be noted that ∠ACB is an angle subtended by the diameter of the circle. Since the angle in a semicircle is a right angle, we have x=∠ACB=90∘