Slice the circle
Two radii cut a circle into a minor sector and a major sector, and their angles add up to 360°.
A pizza cut by two radii
Two cuts from the centre O to the edge of a round pizza make an angle of 70°. The pizza falls into two pieces.
How big is the angle of the bigger piece at O?
What this lesson covers
The idea
A sector is the part of a circular region enclosed by two radii and the corresponding arc; two radii with angle θ between them form a minor sector of angle θ and a major sector of angle 360° – θ.
A pizza cut by two radii
Two cuts from the centre O to the edge of a round pizza make an angle of 70°. The pizza falls into two pieces.
How big is the angle of the bigger piece at O?
- 110°
- 290°
- 70°
Turn B round the circle
Drag B round the rim, or use the dial. The blue piece is the smaller one and the amber piece is the bigger one. Watch both angles.
Two sectors, 360° together
A sector is the part of a circle enclosed by two radii and the arc between them. If the angle between the radii is θ, the minor sector has angle θ and the major sector has angle 360° − θ.
The two sectors fill the whole circle, so their angles add up to 360°. With θ = 70°, the major sector is 360° − 70° = 290°.
The minor sector is the smaller piece, with an angle less than 180°. If OA and OB are in one straight line, both pieces are 180°, half the circle each.
Notes
If the angle between two radii is θ, the minor sector has angle θ and the major sector has angle 360° − θ.
Check yourself
Two radii make a minor sector of 105°. Find the angle of the major sector.
Answer: 255 °
Major sector = 360° − 105° = 255°.
The major sector of a circle has an angle of 310°. Find the angle of the minor sector.
Answer: 50 °
Minor sector = 360° − 310° = 50°.
Two radii of a circle make an angle of 100° between them. Which statement is true?
The radii OA and OB lie in one straight line (A, O, B on a line). What can you say about the two sectors?
- The minor sector is 100° and the major sector is 260°. — correct. Yes! 360° − 100° = 260°, and 260° is the bigger piece.
- The minor sector is 100° and the major sector is 80°.. The major sector is the bigger piece, and 80° is smaller than 100°. The two angles must add up to 360°.
- The minor sector is 260° and the major sector is 100°.. The minor sector is the smaller piece. 100° is smaller than 260°, so 100° is the minor one.
- Both are 180°, half the circle each. — correct. Yes! A straight angle is 180°, and 360° − 180° = 180° too. The two pieces are equal.
- There is no minor sector, only a major one.. Each piece is a half circle, with the same angle, so neither is bigger than the other.
- The minor sector is 0°.. The two radii are not on top of each other. They make a straight angle of 180°.