SME
Grade 10 Math · Geometry
Circles: arcs, chords, tangents and inscribed angles
Use this for “An arc measures 130°. What is the inscribed angle that intercepts it?”
Diagram
An inscribed angle is half the central angle on the same arc.
Inscribed angle: i = c/2 = 130°/2 = 65°
Drag P along the far arc: the angle stays the same.
This is an example. Type your own values to start a new problem.
i
°
=
c
°
÷
2
Formulas
i
=
c
2
65
=
130
2
Assumptions
•
A central angle has its vertex at the center O; it has the same measure as its arc AB.
•
An inscribed angle has its vertex P on the circle and stands on the same arc: it is half the central angle.
•
Every inscribed angle on the same arc is equal, wherever P sits on the other arc.
Step-by-step
WE KNOW
c = 130°
FIND
inscribed angle APB (i)
Step 1 · Find inscribed angle APB (i)
Use i = c ÷ 2
An inscribed angle is half the central angle on its arc.
i
=
130
2
i
=
65°
Check
Put the numbers back in. Both sides should match.
65
=
130
2
✓
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