Angle Formed by Two Intersecting Chords

Angle Formed by Two Intersecting Chords

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

Formula

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

Example

Find the value of x.

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

m∠[brown] = x

The intercepted arcs are 32º and 74º.

So x = (1/2)⋅(32 + 74).

32 + 74 = 106

(1/2)⋅106 = 53

So x = 53.