Question

Diameters AB and CD of circle K intersect such that m∠BKD = 100°. The measure of arc AC is:

Answer 1

The diameters intersect at the center of the circle
m<BKD = 100
<AKC is vertical to <BKD, so m<AKC = 100
An arc has the same measure as its central angle,
so m(arc)AC = 100

Answer 2

Measure of arc AC = 100°

Explanation:

For better understanding of the solution, see the attached figure :

Given : AB and CD are the diameters of the circle K and m∠BKD = 100°

To find : measure of arc AC

Solution :

The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC

Now, m∠BKD = 100°

and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)

⇒ m∠AKC = 100°

Hence, Measure of the arc AC = 100°