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[angle formed by a tangent and a chord] = (1/2) m[intercepted arc]](https://ximpledu.com/en-us/angle-formed-by-a-tangent-and-a-chord/angle-formed-by-a-tangent-and-a-chord-01-02.png "Angle Formed by a Tangent and a Chord: 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.
