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The radian measures of the central angle of the sector is 2
Given,
In the question:
Perimeter of sector is 4 times of its radius .
To find the radian measures of the central angle of the sector is?
Now, According to the question:
We know:
The perimeter of the circumference is = 2r
If the perimeter of a sector is 4 times its radius.
then, the arc measure of the sector is (4r-2r) → 2r
So, if 2× radians (full circle) has a length → 2
r
X radians → 2× r (the sector)
X=2× r ×(2×)/(2
r)
X = 2
Hence, The radian measures of the central angle of the sector is 2.
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