Question 19

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waecmaths question: 

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

Option A: 

45o

Option B: 

60o

Option C: 

75o

Option D: 

90o

waecmaths solution: 

$\begin{align}  & perimeter=\frac{\theta }{{{360}^{\circ }}}\times 2\pi r+2r=\pi +8 \\ & \left( \frac{\theta }{{{360}^{\circ }}}\times 2\pi \times 4 \right)+(2\times 4)=\pi +8 \\ & \frac{\theta }{{{360}^{\circ }}}\times 2\pi \times 4=\pi  \\ & \theta =\frac{{{360}^{\circ }}}{8}={{45}^{\circ }} \\\end{align}$

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