Question

A triangle is shown with its exterior angles. Angles 2, 6, and 4 are the interior angles. Angle 1 is the exterior angle at angle 2. Angle 5 is the exterior angle at angle 6. Angle 3 is the exterior angle at angle 4.
Which statements are always true regarding the diagram? Check all that apply.

m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
m∠4 + m∠6 = m∠2
m∠2 + m∠6 = m∠5

Answer 1

True:
- m∠3 + m∠4 = 180° — ∠3 is the exterior angle at the vertex of ∠4, so they are a linear pair (supplementary).
- m∠2 + m∠4 + m∠6 = 180° — sum of the triangle's interior angles.
- m∠2 + m∠4 = m∠5 — an exterior angle equals the sum of the two remote interior angles (∠5 is opposite ∠2 and ∠4).

False:
- m∠1 + m∠2 = 90° — actually m∠1 + m∠2 = 180° (supplementary), not necessarily 90°.
- m∠4 + m∠6 = m∠2 — would require ∠2 = 180° − ∠2, not generally true.
- m∠2 + m∠6 = m∠5 — m∠5 = m∠2 + m∠4, so this is only true if ∠4 = ∠6, not always.