Question

What fractional part of one semicircle does the labeled angle represent? Express your answer as a fraction in simplest terms. Then, express the labeled angle in radian measure

Answer 1

The fraction of the labelled angle is: 2/3 of one semicircle.

In radians, it is: 2.0944 rad.

Recall:

One semicircle = 3.1416 radian

One semicircle = 180 degrees

Thus, 120 degrees of a semicircle as a fraction would be:

• 120/180 = 2/3

Therefore, 120 degrees equals 2/3 semicircle.

Convert to radians:

One semicircle = 3.1416 radian

2/3 semicircle = x

• Cross multiply

$x = 3.1416 \times \frac{2}{3} \\\\\mathbf{x = 2.0944 rad}$

Therefore, the fraction of the labelled angle is: 2/3 of one semicircle.

In radians, it is: 2.0944 rad.

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