Inscribed angle — Geometry, what it means and where it is taught
An angle whose vertex is on the circle. Half its arc.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Arc — Part of the edge; a "pizza slice" bounded by two radii.
Practise this idea
5 questions in the course bank use Inscribed angle, in Circle Angles, Arcs & Chords.
Problem 1
An inscribed angle cuts an arc of 86°. Find the angle.
Worked answer
43
86 ÷ 2 = 43°
Problem 2
An inscribed angle measures 35°. Find its arc.
Worked answer
70
2 × 35 = 70°
Problem 3
Two inscribed angles stand on the same arc. One is 28°. Find the other.
Worked answer
28
Angles on the same arc are congruent.
28°
Problem 4
A central angle is 124°. Find the inscribed angle on the same arc.
Worked answer
62
124 ÷ 2 = 62°
Problem 5
An inscribed angle is (3x)° and its arc is (8x - 20)°. Find x.
Worked answer
10
8x - 20 = 2(3x)
8x - 20 = 6x
x = 10