The problem provides a pie chart representing the population distribution of men, women, and children in a city. The angles corresponding to women and children are given as $120^\circ$ and $169^\circ$ respectively. The total population of the city is 1,800,000. We need to find the number of men in the city.

1. Problem Description

The problem provides a pie chart representing the population distribution of men, women, and children in a city. The angles corresponding to women and children are given as $120^\circ$ and $169^\circ$ respectively. The total population of the city is 1,800,

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0. We need to find the number of men in the city.

2. Solution Steps

First, we need to find the angle corresponding to the men's population. Since the total angle in a circle is $360^\circ$, we have:

Angle for Men = Total Angle - Angle for Women - Angle for Children

Angle for Men = $360^\circ - 120^\circ - 169^\circ = 71^\circ$

Next, we need to find the fraction of the population that corresponds to men. This is the angle for men divided by the total angle:

Fraction of Men = $\frac{\text{Angle for Men}}{360^\circ} = \frac{71^\circ}{360^\circ}$

Finally, we multiply this fraction by the total population to find the number of men in the city:

Number of Men = Fraction of Men $\times$ Total Population

Number of Men = $\frac{71}{360} \times 1,800,000 = 71 \times 5000 = 355,000$

3. Final Answer

The number of men in the city is 355,

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0. Answer: C. 355,000