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The perimeter of a sector of a circle of radius 4cm is (\(\p...

The perimeter of a sector of a circle of radius 4cm is ( $\pi + 8$ )cm. Calculate the anle of the sector

A.

45^o

B.

60^o

C.

75^o

D.

90^o

View answer & explanation

Correct answer is A

Perimeter of sector = 2r + $\frac{\theta}{360^o} \times 2\pi r$

$\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4$

$\pi + 8 + \frac{\theta}{360^o} \times 8 \pi$

P + 8 - 8 = $\frac{\theta \pi}{456o}$

$\pi = \frac{\theta \pi}{45^o}$

$\theta \pi = 45^o$

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