Angle Formed by a Tangent and a Secant

Angle Formed by a Tangent and a Secant

How to find the measure of the angle formed by a tangent and a secant: formula, example, and its solution.

Formula

m[angle formed by a tangent and a secant] = (1/2)*(m[intercepted arc 1] - m[intercepted arc 2])

m∠[brown] = (1/2)(m[blue arc] - m[green arc])

∠[brown]: Angle formed by a tangent and a secant
[blue arc], [green arc]: Intercepted arcs

Example

Find the value of x.

The brown angle is the angle
formed by a tangent and a secant.

m∠[brown] = x

The intercepted arcs are 143º and 63º.

So x = (1/2)⋅(143 - 63).

143 - 63 = 80

(1/2)⋅80 = 40

So x = 40.