Question

angle ACB is inscribed in and arc ACB of a circle with center O .if angle ACB =65° then find the measure of angle AOB​

Answer 1

Step-by-step 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°

I hope this helps!