Question

The perimeter of a sector of a circle is equal to the
length of the semicircle of the circle. Find the measure
of its angle in radians.​

Answer 1

Step-by-step explanation:

theta = arc / radius

here , perimeter of sector = length of semicircle of the circle

perimeter of sector =length of arc + length of two radii

πr = length of arc + 2r

πr - 2r = length of arc

Theta = arc length / radius

= πr - 2r / r

= π - 2

Answer 2

Given ,

The perimeter of a sector of a circle is equal to the length of the semicircle of the circle

We know that , the perimeter of a sector of a circle is given by

$\large \mathtt{\fbox{Perimeter \: of \: sector = \frac{ \theta}{360} \times 2 \pi r }}$

and the perimeter of semicircle is given by

$\mathtt{\large\fbox{Perimeter \: of \: semicircle =\pi r}}$

According to the question ,

$\sf \hookrightarrow \frac{ \theta}{360} \times 2 \pi r = \pi r \\ \\\sf \hookrightarrow \theta = \frac{360}{2} \\ \\\sf \hookrightarrow \theta = 180$

Hence , the angle is 180° degrees

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