Angle Formed by Two Chords

How to find the angle formed by two intersecting chords of a circle: formula, 1 example, and its solution.

Formula

Formula

θ = [1/2](m[arc AC] + m[arc BD])

θ: Angle formed by two intersecting chords
arc AC: The same side arc
arc BD: The opposite side arc

Example

Example

Solution

xº is the angle
formed by two intersecting chords AB and CD.

The same side arc is 74º.
The opposite side arc is 32º.

So x = [1/2]⋅(74 + 32).

74 + 32 = 106

[1/2]⋅106 = 53

So 53 is the answer.