The lengths of the minor and major arcs 54cm and 126cm respectively. Calculate the angle…

The lengths of the minor and major arcs 54cm and 126cm respectively. Calculate the angle of the major sector

Correct Answer: Option B

Explanation

Let 0 = angle of the minor sector
angle of the major sector = 360 – (theta)(angle at a point)
2 (pi r) = 54 + 126(i.e circumference of minor and major arc)
2(pi r = 180^o)
r = (frac{180}{2pi}) = (frac{90}{pi})
Lenght of ninor arc
= (frac{theta}{360} times 2 pi r)
54 = (frac{theta}{360} times 3 pi r)
(theta = frac{360 times 54}{2 pi r})
but r = (frac{90}{pi}) substituting (frac{90}{pi}) for r
(theta = frac{360 times 54 times pi}{2 times pi times 90})
(theta = 2 times 54 = 108^o)
angle of the major sector = 360 – 108^o
= 252^o