 The circle graph above shows U.S. production of photographic equipment and supplies in 1971, with the largest sector, **Sensitized Goods**, representing $47\%$ of total production. What is the **measure of the central angle** of the Sensitized Goods sector, to the nearest degree?
A$47^{\circ}$
B$90^{\circ}$
C$169^{\circ}$
D$180^{\circ}$
Answer & Solution
Correct answer: C. $169^{\circ}$
In a circle graph, each sector's central angle is **proportional to its percent of the whole**: an angle of $360^{\circ}$ corresponds to $100\%$.
So the angle for Sensitized Goods is:
$0.47 \times 360^{\circ} = 169.2^{\circ} \approx 169^{\circ}$.
- Trap A ($47^{\circ}$) confuses *percent* with *degrees* directly.
- Trap B ($90^{\circ}$) treats every sector as a quarter circle.
- Trap D ($180^{\circ}$) would require the sector to be exactly half — but $47\%$ is just under half.
Visual sanity check on the figure: the Sensitized Goods sector clearly spans just less than half the circle, consistent with an angle of about $169^{\circ}$.
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