# Angle Formed by a Tangent and a Chord

How to find the measure of the angle formed by a tangent and a chord: formula, examples, and their solutions.

## Formula

m∠[brown] = (1/2) m[blue arc]

∠[brown]: Angle formed by a tangent and a chord

[blue arc]: Intercepted arc

## Example 1

m∠[brown] is the angle

formed by a tangent and a chord.

Arc *AB* is the intercepted arc.

m∠[brown] = *x*

m[arc *AB*] = 110

So *x* = (1/2)⋅110.

(1/2)⋅110 = 55

So *x* = 55.

## Example 2

m∠[brown] is the angle

formed by a tangent and a chord.

The blue arc is the intercepted arc.

m∠[brown] = *x*

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

This brown angle is the inscribed angle

whose intercepted arc is the same blue arc.

m∠[brown] = 80

So (1/2) m[blue arc] = 80.

Inscribed angle

*x* = (1/2) m[blue arc] = 80

So *x* = 80.