Question

If the angle of the major sector of a circle is 250°, then find the angle of the minor sector (in degrees).

Answer 1

Hint:: We need to find the area of the minor sector provided the area of the major sector of a given circle. We will use the formula: Angle of minor sector + Angle of major sector = 360° to find the area of the minor sector of the given circle.

Complete step by step Answer:

We are given that the angle of the major sector of a circle is 250°.
We know that the total angle of the sector in a circle is 360°.
By using the formula: Total angle of the sector= angle of the major sector + angle of the minor sector, we can calculate the required area of the minor sector of the circle. Therefore, we get:
$\Rightarrow {360}^{\circ }={250}^{\circ }+$angle of minor sector
$\Rightarrow {360}^{\circ }-{250}^{\circ }={110}^{\circ }=$angle of minor sector
Hence, the angle of the minor sector (in degrees) of a circle whose angle of the major sector is 250° is found to be 110°.

Note: In such questions where we are given an initial value, we just analyze which formulae are related and then apply them taking an account of the desired solution. In this case, we were initially provided with the angle of the major sector, so it became easier for us for calculating the angle of the minor sector without even knowing the radius of the circle or the arc length to calculate the minor angle of the sector of the circle.