Question

angle abc is inscribed in arc of circle with Centre O if measure
angle ACB is equal to 65 find major Arc ACB

Answer 1

Answer:  $230^{\circ}$

Step-by-step explanation:

Since, Here the angle abc is inscribed in arc of circle with Center O,

Also, $m\angle ACB = 65^{\circ}$

⇒ By the Central angle theorem,

$m\angle ABC = 2 \times m\angle ACB = 2 \times 65^{\circ} = 130^{\circ}$

Thus, the length of major arc ACB = $360^{\circ} - 130^{\circ} = 230^{\circ}$

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°