Question

which statements are always true regarding the diagram? select three options. □ $m\angle5 + m\angle3 = m\angle4$ □ $m\angle3 + m\angle4 + m\angle5 = 180\degree$ □ $m\angle5 + m\angle6 =180\degree$ □ $m\angle2 + m\angle3 = m\angle6$ □ $m\angle2 + m\angle3 + m\angle5 = 180\degree$

Explanation:

Step1: Check linear pair

∠5 and ∠6 are adjacent and form a straight line, so their sum is 180°. Thus, \(m\angle5 + m\angle6 = 180^\circ\) is true.

Step2: Check triangle angle sum

The triangle with angles 2, 3, 5 has interior angles summing to 180°. Thus, \(m\angle2 + m\angle3 + m\angle5 = 180^\circ\) is true.

Step3: Check exterior angle theorem

∠4 is an exterior angle of the triangle, equal to the sum of remote interiors ∠2 and ∠5? No, wait: ∠3 + ∠4 = 180° (linear pair). The triangle's angles: ∠2 + ∠3 + ∠5 = 180°, so ∠2 + ∠5 = 180° - ∠3 = ∠4. But the option says ∠5 + ∠3 = ∠4? No. Wait, another: ∠6 is exterior to the triangle, so ∠6 = ∠2 + ∠3 (exterior angle = sum of remote interiors). Thus, \(m\angle2 + m\angle3 = m\angle6\) is true.

Answer:

\(m\angle5 + m\angle6 = 180^\circ\), \(m\angle2 + m\angle3 = m\angle6\), \(m\angle2 + m\angle3 + m\angle5 = 180^\circ\)