Question

Angle acb is inscribed in arc acb of a circle .if angle acb is 65 then m(arcacb=?)

Answer 1

may this help u......

Answer 2

Answer:

Measure of major arc ACB = 360 - 130 = 230°

Step-by-step explanation:

Foe better understanding of the solution, see the attached figure of the problem :

Given that the angle ABC is inscribed in arc of circle with center O.

m∠ACB = 65°

Thus, by the central angle theorem which states that the angle formed at the center is twice the angle subtended by the same arc at the circumference of the circle.

⇒ m∠AOB = 2 × m∠ACB

⇒ m∠AOB = 2 × 65°

⇒ m∠AOB = 130°

Now, measure of the major arc ACB can be calculated by subtracting the measure of central angle from a complete angle i.e. 360°

Hence, Measure of major arc ACB = 360 - 130 = 230°