The three options are
- m∠5 + m∠6 = 180° Linear Pair
- ∠ 2+ ∠ 3 = ∠ 6 Exterior angle Property of Triangle
- m∠2 + m∠3 + m∠5 = 180° Triangle Sum Property
Consider Δ ABC with Exterior angles as
∠ 1 , ∠ 4 ,and ∠ 6
Exterior angle Property of Triangle:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠ 1 we have
∠ 1 = ∠ 5 + ∠ 3 Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 4 we have
∠ 4 = ∠ 5 + ∠ 2 Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 6 we have
∠ 6 = ∠ 2 + ∠ 3 Exterior angle Property of Triangle
Triangle Sum Property:
In a triangle sum of the measures of angles is equal to 180°
∴ m∠2 + m∠3 + m∠5 = 180° Triangle Sum Property
Linear Pair:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
∴ m∠5 + m∠6 = 180° Linear Pair