To find the angle of a sector, we can use the formula:

Angle = (Area of Sector / Area of Circle) x 360°

Given that the radius of the circle is 18 cm and the area of the sector is 72 cm², we can proceed with the following steps:

1. Calculating the area of the circle:
The formula for the area of a circle is: Area = πr²
Substituting the radius, we can find the area: Area = π(18 cm)² = 324π cm²

2. Calculating the angle of the sector:
Using the formula mentioned above, we can calculate the angle:
Angle = (72 cm² / 324π cm²) x 360°
Simplifying, we have: Angle = 360°/4π

To further simplify, we divide both the numerator and denominator by 4:
Angle = 90°/π

3. Converting the angle to degrees:
To convert the angle from radians to degrees, we can use the conversion factor:
180° = π radians

Multiplying both sides by the angle in radians, we get:
Angle (in degrees) = (90°/π) x (180°/π)
Angle (in degrees) = 90° x 180° / π²

Simplifying, we have:
Angle (in degrees) ≈ 5174.87°

Therefore, the angle theta (θ) is approximately 5174.87°.

Note: It is important to remember that the area of the sector is given in square units, while the radius and angle are in linear units and degrees, respectively.