Question

If he area of a sector of a circle is $\frac{7}{20}$ of the area of the circle, then the sector angle is equal to
(a)110°
(b)130°
(c)100°
(d)126°

Answer 1

Answer:

The sector angle of a circle is 126°.

Among the given options option (d) 126°  is the correct answer.

Step-by-step explanation:

Given :

Area of a sector of a circle is 7/20 the area of the circle.

Area of a sector of a circle = 7/20 × area of the circle.

θ/360 × πr² = 7/20 × πr²

θ/360 = 7/20  

20 θ = 360 × 7

θ = (360 × 7)/20

θ = 18 × 7  

θ = 126°  

Sector angle of a circle = 126°

Hence, the sector angle of a circle is 126°.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

Let radius of the circle= r

Sector angle = x°

_______________________

i) Area of the circle = πr²

ii) Area of the sector =

(x/360)×πr²

_______________________

According to the problem given,

Area of the sector = (7/20) × Area of the circle

=> (x/360)×πr² = (7/20)×πr²

=> x/360 = 7/20

=> x = (7×360)/20

=> x = 7 × 18

=> x = 126°

Therefore,

Option (d) is correct.

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