Arc — Grade 7 Math, what it means and where it is taught
Part of the edge; a "pizza slice" bounded by two radii.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Central angle — An angle whose vertex is the centre. Equal to its arc.
- Inscribed angle — An angle whose vertex is on the circle. Half its arc.
- Radian — The angle whose arc length equals the radius. A full turn is 2π radians.
Practise this idea
16 questions in the course bank use Arc, in Geometric Construction, Circles, Circle Angles, Arcs & Chords, Radians & the Unit Circle. The first 8 are below; the rest are in those units.
Problem 1
When bisecting an angle with a compass, why must the compass width stay the same for the two final arcs?
- So the drawing looks neat
- So the crossing point is the same distance from both sides
- So the arcs fit on the page
- It does not actually matter
Worked answer
So the crossing point is the same distance from both sides
Equal radii put the crossing point the same distance from each side of the angle.
A point equidistant from both sides lies exactly on the bisector — that is what makes the construction a proof, not a guess.
Problem 2
Find the arc length of a quarter circle of radius 8, in terms of π (enter just the number in front of π).
Worked answer
4
Full circumference: 16π
A quarter: 4π
Problem 3
Find the arc length of a 90° sector of a circle with radius 10. Use π ≈ 3.14.
Worked answer
15.7
Full circumference: 2 × 3.14 × 10 = 62.8
14 × 62.8 = 15.7
Problem 4
A central angle cuts an arc of 70°. Find the angle.
Worked answer
70
70°
Problem 5
An inscribed angle cuts an arc of 86°. Find the angle.
Worked answer
43
86 ÷ 2 = 43°
Problem 6
An angle is inscribed in a semicircle. Find its measure.
Worked answer
90
The arc is 180°.
Half is 90°.
Problem 7
An inscribed angle measures 35°. Find its arc.
Worked answer
70
2 × 35 = 70°
Problem 8
An angle with its vertex at the centre equals
- its arc
- half its arc
- twice its arc
- half the difference
Worked answer
its arc
At the centre, so it equals the arc.