Question

this question requires at least 3 answers. which statements are always true regarding the diagram? choose three correct answers. m∠2 + m∠3 + m∠5 = 180°. m∠3 + m∠4 + m∠5 = 180°. m∠2 + m∠3 = m∠6. m∠5 + m∠3 = m∠4. m∠5 + m∠6 = 180°

Explanation:

Step1: Recall triangle - angle sum property and exterior - angle property

The sum of the interior angles of a triangle is 180°. An exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Analyze the first option

For a triangle with interior angles ∠2, ∠3, and ∠5, by the angle - sum property of a triangle, \(m\angle2 + m\angle3+m\angle5 = 180^{\circ}\). This is true.

Step3: Analyze the second option

\(m\angle3 + m\angle4+m\angle5
eq180^{\circ}\) because ∠4 is an exterior angle. The sum of the interior angles of a triangle is 180°, and ∠4 is not an interior angle of the triangle with interior angles ∠3 and ∠5. This is false.

Step4: Analyze the third option

∠6 is an exterior angle of the triangle with non - adjacent interior angles ∠2 and ∠3. By the exterior - angle property of a triangle, \(m\angle2 + m\angle3=m\angle6\). This is true.

Step5: Analyze the fourth option

∠4 is an exterior angle of the triangle with non - adjacent interior angles ∠3 and ∠5. By the exterior - angle property of a triangle, \(m\angle5 + m\angle3=m\angle4\). This is true.

Step6: Analyze the fifth option

∠5 and ∠6 are not supplementary in general. They are angles formed at a vertex outside the triangle and do not have a fixed sum of 180°. This is false.

Answer:

\(m\angle2 + m\angle3 + m\angle5=180^{\circ}\), \(m\angle2 + m\angle3=m\angle6\), \(m\angle5 + m\angle3=m\angle4\)