waecmaths question:
The perimeter of a sector of a circle of radius 21cm is 64cm. Find the angle of the sector. Take [$\pi=\tfrac {22}{7}$ ].
Option A:
70o
Option B:
60o
Option C:
55o
Option D:
42o
waecmaths solution:
$\begin{align} & Perimeter=\frac{\theta }{{{360}^{\circ }}}\times 2\pi r+2r \\ & 64=\frac{\theta }{{{360}^{\circ }}}\times 2\times \frac{22}{7}\times 21+2(21) \\ & 64=\frac{\theta }{360}\times 132+42 \\ & 22=\frac{\theta }{{{360}^{\circ }}}\times 132 \\ & \theta =\frac{22}{132}\times {{360}^{\circ }}={{60}^{\circ }} \\\end{align}$
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