Angle Formed by a Tangent and a Chord

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]

m∠[brown] = (1/2) m[blue arc]

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

Example 1

If the measure of arc AB is 110, find the value of x.

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

Find the value of x.

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.