Question

find x in the following please
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Answer 1

Calculation of Angle substended by arc at center of circle.

Answer: Required value of x is 40°.

Explanation:

Given that

angle subtended by minor arc AC at center of circle that is ∠AOC = x°.

angle subtended by minor arc AC on circumfrence of the circle ∠ABC =20°.

Need to determine value of x.

Here we will be using theorem which says that "Angle subtended by arc on the center of circle is doubled that angle substended by same arc on any point on circumference of circle."

using above theorem we van say that

Angle subtended by minor arc AC at center = 2 × Angle substended by minor arc AC at any point on circumfrence of circle

⇒ ∠AOC = 2 × ∠ABC

⇒ x° = 2 × 20°

⇒ x = 40°

Hence required value of x is 40°.

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