Lesson 4: Angles and Chords

Intersection of 2 Chords

• 4 angles

• 4 arcs

The measure of an angle created by 2 intersecting chords in a circle can be found by taking half of the sum of of the arcs made by the angle and the vertical angle of the original arc.

Example: If a circle has chords AC and BD which intersect at point E, angle AED (let’s name it angle 1)’s degree measure can be found by adding the measurements of arcs AD and BC and then dividing that by 2.

Angle 1 = ½ (arc AD + arc BC)

Intersection of 2 Secants, Tangents, or One of Both

Note: The angle made by the lines at which they intersect will be outside of the circle. It can be found by taking the difference of the smaller arc subtracted from the larger arc and then dividing it by half.

Angle X = ½ (y-x)

    Where y is the larger arc and x is the smaller arc.