Question

Angle ACB is inscribed in a arc ACB of a circle with centre O. If angle ACB =65° find m(arc ACB)

Answer 1

m(arc ACB)=230°

Explanation:

Given : ∠ACB is inscribed in a arc ACB of a circle with centre O.

∠ACB =65°

The Inscribed Angle Theorem : The measure of an inscribed angle is half the measure the arc intercepted by it.

Therefore , ∠ACB= half of Measure of arc AB

⇒Measure of arc AB = 2 x  ∠ACB = 2 x 65° =130°

Since arcAB is minor arc and arc ACb is major arc and tyhe sum of minor and major arc is 360°.

⇒ Measure of Major arc = 360°- Minor arc

⇒ Measure of arc ACB = 360°  -130°  

=230°

Hence, m(arc ACB) =230°

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