Question

Which of the following is true about the major sector?
This question has multiple correct answers.
A. A major sector has a central angle which is more than ${{270}^{\circ }}$ .
B. A larger part occupied by two radii.
C. A major sector has a central angle which is more than ${{180}^{\circ }}$ .
D. All of the above.

Answer 1

Hint: A pair of radii divide a circle into two sectors.
The two sectors can be either both equal, or one greater than the other.
A circle is a complete rotation and hence the central angle of a circle is ${{360}^{\circ }}$ .

Complete step-by-step answer:
The two sectors formed by two radii of a circle are shown in the following diagram:

Let us look at the answer options one by one and check if they are correct:
A. A major sector has central angle which is more than ${{270}^{\circ }}$ .: Since, the major sector has an angle more than ${{180}^{\circ }}$ , it is still possible to have a sector with angle less than ${{270}^{\circ }}$ to be a major sector, for example ${{200}^{\circ }}$ . The statement is not correct.
B. A larger part occupied by two radii.: The two radii divide a circle into two parts in which one is larger and the other is smaller if they are not both equal. The larger part is called the Major Sector. So yes, this is also correct.
C. A major sector has central angle which is more than ${{180}^{\circ }}$ .: From the above diagram, it can be seen that the major sector has angle more than ${{180}^{\circ }}$ . Hence, correct.
D. All of the above.: Since A is incorrect, this statement is not correct.
Hence, only statements B. and C. are correct.
Note: The statement "A sector with central angle more than ${{270}^{\circ }}$ is a Major Sector." is correct but "A Major Sector has a central angle more than ${{270}^{\circ }}$ ." is not necessary .