### Theory:

Since pie charts are circular, they are formed using a $$360^\circ$$ angle.

Pie charts, as a whole, constitute $$100\%$$.

Each component on the pie chart occupy some parts of the entire pie chart. The parts that each of the components occupy are represented as percentages.

The volume of each of the components on a pie chart is found using the formulae given below.
$$\text{The central angle of the component} = \frac{\text{Value of the component}}{\text{Total value}} \times 360^\circ$$
If the components are expressed as percentages, then:
$$\text{The central angle of the component} = \frac{\text{Percentage value of the component}}{100} \times 360^\circ$$
Now, let us try to construct a pie chart for the given values.

Component $$1 = 15000$$

Component $$2 = 5000$$

Component $$3 = 10000$$

Component $$4 = 2500$$

Component $$5 = 7500$$

First, find the portion each of the individual components occupy on the pie chart.

Since, values are considered in this example, use the following formula:

$$\text{The central angle of the component} = \frac{\text{Value of the component}}{\text{Total value}} \times 360^\circ$$

Here, the total value is the sum of all the values of the individual components.

Total value $$=$$ Value of component $$1 +$$ Value of component $$2 +$$ Value of component $$3 +$$ Value of component $$4 +$$ Value of component $$5$$

$$= 15000 + 5000 +10000 + 2500 + 7500$$

$$= 40000$$

$$\text{The central angle of the component 1} = \frac{15000}{40000} \times 360^\circ$$

$$= 135^\circ$$

Now, the centre of the pie chart as radius, construct an angle of $$135^\circ$$.

$$\text{The central angle of the component 2} = \frac{5000}{40000} \times 360^\circ$$

$$= 45^\circ$$

Now, the centre of the pie chart as radius, construct an angle of $$45^\circ$$.

$$\text{The central angle of the component 3} = \frac{10000}{40000} \times 360^\circ$$

$$= 90^\circ$$

Now, the centre of the pie chart as radius, construct an angle of $$90^\circ$$.

$$\text{The central angle of the component 4} = \frac{2500}{40000} \times 360^\circ$$

$$= 22.5^\circ$$

Now, the centre of the pie chart as radius, construct an angle of $$22.5^\circ$$.

$$\text{The central angle of the component 5} = \frac{7500}{40000} \times 360^\circ$$

$$= 67.5^\circ$$

Now, the centre of the pie chart as radius, construct an angle of $$67.5^\circ$$ to complete the pie chart.