Question

which statements are always true regarding the diagram? select three options.

\\(m\angle 5 + m\angle 3 = m\angle 4\\)
\\(m\angle 3 + m\angle 4 + m\angle 5 = 180^{\circ}\\)
\\(m\angle 5 + m\angle 6 = 180^{\circ}\\)
\\(m\angle 2 + m\angle 3 = m\angle 6\\)
\\(m\angle 2 + m\angle 3 + m\angle 5 = 180^{\circ}\\)

Explanation:

Analyze the triangle interior angles

The diagram shows a triangle with interior angles \(\angle 2\), \(\angle 3\), and \(\angle 5\).
Using the Triangle Angle Sum Theorem:

$$ m\angle 2 + m\angle 3 + m\angle 5 = 180^\circ $$

This matches the fifth statement.

Analyze linear pairs

At vertex \(C\), \(\angle 5\) and \(\angle 6\) form a linear pair along the straight line.
Using the Linear Pair Postulate:

$$ m\angle 5 + m\angle 6 = 180^\circ $$

This matches the third statement.

Analyze exterior angles

At vertex \(C\), \(\angle 6\) is an exterior angle to the triangle.
Using the Exterior Angle Theorem, the measure of an exterior angle equals the sum of its two remote interior angles:

$$ m\angle 2 + m\angle 3 = m\angle 6 $$

This matches the fourth statement.

Answer:

• ☐ \(m\angle 5 + m\angle 3 = m\angle 4\)
• ☐ \(m\angle 3 + m\angle 4 + m\angle 5 = 180^\circ\)
• ☑ \(m\angle 5 + m\angle 6 = 180^\circ\) (Correct answer)
• ☑ \(m\angle 2 + m\angle 3 = m\angle 6\) (Correct answer)
• ☑ \(m\angle 2 + m\angle 3 + m\angle 5 = 180^\circ\) (Correct answer)