Angle Formed by Two Intersecting Tangents

Angle Formed by Two Intersecting Tangents

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

Formula

m[angle formed by two intersecting tangents] = (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 tangents
[blue arc], [green arc]: Intercepted arcs

Example

Find the value of x.

The blue arc and the green arc
form a circle.

m[green arc] = 130

So 130 + m[blue arc] = 360.

Move +130 to the right side.

Then m[blue arc] = 230.

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

m∠[brown] = x

The intercepted arcs are 230º and 130º.

So x = (1/2)⋅(230 - 130).

230 - 130 = 100

(1/2)⋅100 = 50

So x = 50.