Question

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?

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

Answer 1

m∠1 + m∠2 = 180° is true.

Reason: each exterior angle is a linear pair with its adjacent interior angle, so m∠1 and m∠2 are supplementary. The other choices are not generally true (e.g. m∠1 = m∠3 + m∠5, m∠6 = m∠2 + m∠3, and m∠2+m∠3+m∠5 = 180°, so the listed alternatives do not hold in general).