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An arc of a circle of length 22 cm subtends an angle of 3x$$^{\circ}$$ at the ce...

Question

An arc of a circle of length 22 cm subtends an angle of 3x$$^{\circ}$$ at the center of the circle. Find the value of x if the diameter of the circle is 14 cm

Options

A) 60$$^{\circ}$$

B) 120$$^{\circ}$$

C) 180$$^{\circ}$$

D) 30$$^{\circ}$$

$$ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}$$
• $$ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}$$