Question

If O is the centre of the circle, find the value of x in each of the the following .​

Answer 1

In the given picture, We have,

⇒ ∠AEC = 40°

⇒ ∠ACE = 90° [ ∵ Angle subtended by the diameter of a circle on the circle measures 90° ]

Now, In △ACE,

⇒ ∠CAE + ∠ACE + ∠AEC = 180° [ ∵ Sum of all interior angles of a triangle is 180° ]

⇒ ∠CAE + 90° + 40° = 180° [ given ]

⇒ ∠CAE = 180° - 130°

⇒ ∠CAE = 50° ...(1)

Again, Angles subtended by an arc on the circle are equal.

∴ ∠CAE = x [ Angles subtended on the circle by the same arc ]

⇒ x = 50° [ from (1) ]

Hence, Value of x is 50°

Some Information :-

☛ Angle subtended at the centre of a circle is double the angle subtended on the circle by the same arc.

☛ The diameter of a circle subtends an angle of 90° on the circle.