Question

which is a true statement about the diagram?
o m∠5 + m∠6 + m∠1
o m∠3 + m∠4 + m∠5 = 180°
o m∠1 + m∠2 = 180°
o m∠2 + m∠3 = m∠6

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle formed by angles 3, 4, and 5, we have the relationship based on this property.

Step2: Analyze each option

• Option 1: There is no geometric relationship that would imply \(m\angle5 + m\angle6=m\angle1\) in general.
• Option 2: Since \(\angle3\), \(\angle4\), and \(\angle5\) are the interior angles of a triangle, by the angle - sum property of a triangle, \(m\angle3 + m\angle4 + m\angle5=180^{\circ}\).
• Option 3: \(\angle1\) and \(\angle2\) are not supplementary in the given diagram.
• Option 4: There is no such angle - addition relationship \(m\angle2 + m\angle3=m\angle1\) based on the standard geometric angle properties.

Answer:

\(m\angle3 + m\angle4 + m\angle5 = 180^{\circ}\)