 # Inscribed Angle How to find the inscribed angle of a circle: definition, formula, examples, and their solutions.

## Definition An inscribed angle is an angle
whose vertex is on the circle
and whose sides are the chords of the circle.

Chord of a circle

## Formula m∠[brown] = (1/2) m[blue arc]

∠[brown]: Inscribed arc
[blue arc]: Intercepted arc

## Example 1 m∠[blue] = 80

So m[blue arc] = 80.

Measure of an arc

m[blue arc] = 80

So x = (1/2)⋅80.

(1/2)⋅80 = 40

So x = 40.

## Example 2 m∠[brown] = 100

So 100 = (1/2) m[arc ABC].

Switch both sides.

Multiply 2 on both sides.

Then m[arc ABC] = 200.

## Example 3 This brown angle is an inscribed angle
whose intercepted arc is the blue arc.

m∠[brown] = [7x + 1]

So [7x + 1] = (1/2) m[blue arc].

This brown angle is also an inscribed angle
whose intercepted arc is the same blue arc.

m∠[brown] = [3x + 29]

So (1/2) m[blue arc] = [3x + 29].

Both brown angles
have the same intercepted arc.

So [7x + 1] = [3x + 29].

Move 3x to the left side.
And move +1 to the right side.

Then, 7x - 3x, 4x
is equal to,
+29 - 1, 28.

Divide both sides by 4.

Then x = 7.