# Angle Formed by Two Intersecting Chords

How to solve problems about the angle formed by two intersecting chords: formula, proof, example, and its solution.

## Formula

m∠(red) = (1/2)⋅(m[blue arc] + m[green arc])

∠(red): angle formed by two chords

blue & green arcs: intercepted arcs

## Proof

Draw a chord to make a triangle.

(gray trangle)

m∠(green) = (1/2)⋅m[green arc]

m∠(blue) = (1/2)⋅m[blue arc]

Inscribed angle

See the gray triangle.

The red angle is the exterior angle of the gray triangle.

So m∠(red) = (1/2)⋅m[blue arc] + (1/2)⋅m[green arc].

So m∠(red) = (1/2)⋅(m[blue arc] + m[green arc]).

## Example

m∠(red) = *x*, m[blue arc] = 32, m[green arc] = 74*x* = (1/2)⋅(32 + 74)