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Problem 1: A circular pizza into 3 equal parts, one piece of pizza is taken out. Estimate the degree measure of the single piece of pizza convert the measure into radians. What is the radian measure of the angle of the remaining part of pizza?

Solution

The circular pizza is makes an angle of 3600 and when it is divided into three equal parts, each part is an angle of 1200. According to the statement of the problem, one part (= 1200) is taken out and the remaining portion is 1200 + 1200 = 240

Hence, to find the radian measure of the part taken out, we have,

570 = 1 rad

Divide both sides by 57,

Now multiply both sides by 120.

(Note: The small discrepancy is due to the conversion values. In fact, 57.30 = 1 rad. Take this value of conversion and get the exact answer).

Similarly, the remaining part is double of the part taken out. Therefore,

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