Inscribed angle in a circle, step by step
Two angles standing on the same arc: one at the center of the circle, one out on the rim.
The question
degrees
Center angle 40°, find the angle on the circle
same arc, two angles
center = 2 × circlesocircle = center ÷ 2
40 ÷ 2=20
- Both marked angles stand on the SAME arc — the two chords and the two radii end at the same two points on the circle. That is what makes them a pair; two angles in a circle that do not share an arc have nothing to say to each other.
- The angle at the CENTER is always twice the one on the circle, wherever on the far arc that point sits. Here the center angle is the one given, so this is a halving.
- Half of 40 is 20, so the angle on the circle is 20°.
How it works.
- 01
Both marked angles stand on the SAME arc — the two chords and the two radii end at the same two points on the circle. That is what makes them a pair; two angles in a circle that do not share an arc have nothing to say to each other.
- 02
The angle at the CENTER is always twice the one on the circle, wherever on the far arc that point sits. Here the center angle is the one given, so this is a halving.
- 03
Half of 40 is 20, so the angle on the circle is 20°.