Angle Formed by Two Intersecting Secants

Angle Formed by Two Intersecting Secants

How to find the measure of the angle formed by two intersecting secants: formula, example, and its solution.

Formula

m[angle formed by two intersecting secants] = (1/2)*(m[intercepted arc 1] - m[intercepted arc 2])

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

∠[brown]: Angle formed by two intersecting secants
[blue arc], [green arc]: Intercepted arcs

Example

Find the value of x.

The brown angle is the angle
formed by two intersecting secants.

m∠[brown] = x

The intercepted arcs are 108º and 44º.

So x = (1/2)⋅(108 - 44).

108 - 44 = 64

(1/2)⋅64 = 32

So x = 32.