In a circle with radius of 7 cm, an arc of the circle has length 22 cm.

The central angle theta is ??

Angle θ = arc length / radius,

=22/7
= π approx. (in radians).

To find the central angle theta, we can use the formula:

Arc length = (Central angle / 360) * (2 * pi * Radius)

Given:
Arc length = 22 cm
Radius = 7 cm

Let's plug in the values and solve for theta:

22 cm = (Central angle / 360) * (2 * pi * 7 cm)

First, simplify the equation:

22 cm = (Central angle / 360) * (14 * pi cm)

Next, let's get rid of the fraction by multiplying both sides of the equation by 360:

22 cm * 360 = Central angle * (14 * pi cm)

7920 cm = Central angle * 14 * pi cm

Divide both sides of the equation by (14 * pi) to solve for the central angle:

Central angle = (7920 cm) / (14 * pi cm)

Finally, simplify the expression:

Central angle = 180 cm / pi

Therefore, the central angle theta is approximately equal to 57.3 degrees.