Grade 7 › G7U07 Circles & Area

Grade 7 › G7U07 Circles & Area › L3
GRADE 7 · ALBERTAOUTCOME AB-G7-SS1

L3 · Central angles: they sum to 360 degrees

Learning goal

“I can identify a central angle and the sector it cuts, and I can find a missing central angle because all the central angles around a centre always sum to 360°.”

Central angle — an angle whose vertex (corner point) is at the centre of a circle and whose sides are radii.
Sector — the wedge (pie-slice) region of a circle cut out by two radii and the arc between them. A central angle and its sector always match: bigger angle, bigger slice.
Vertex — the corner point where the two sides of an angle meet. For a central angle, the vertex is the centre of the circle.
Worked example

A pizza is cut into 4 equal slices by two diameters crossing at the centre. Step 1: Each slice is a sector. Each slice's angle has its vertex at the centre and radii for sides - each is a central angle. Step 2: Walking around the centre, the 4 angles fill one complete turn with no gaps and no overlaps: their sum is exactly 360°. Step 3: The slices are equal, so each central angle is 360 / 4 = 90°. Say it plainly: central angles behave like slices of one whole pie - however you cut the circle from the centre, the angles around the centre always add to 360°.

Check yourself — explain it

What makes an angle a CENTRAL angle?

Paired problem — example still visible

A pie is cut into 5 equal slices. Each slice's central angle? -> 72° (360 / 5)

Faded completion — last step is yours

"A circle is cut into 8 equal sectors. Each central angle is 360 / 8 = ___°" -> 45°

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