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 statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°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 statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answer 1

Answer:

In the given Triangle problem, the three options are:

1.  m∠5 + m∠6 = 180°

2. ∠2+ ∠3 = ∠6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept: Consider Δ ABC with Exterior angles ∠1, ∠4 and ∠6.

Use the Exterior angle Property of Triangle which says that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior angle ∠1 we have:

∠1 = ∠5 + ∠3

Similarly, for Exterior ∠4 we have:

∠4 = ∠5 + ∠2

Similarly, for Exterior ∠6 we have:

∠6 = ∠2 + ∠3

Now, use the Triangle Sum Property which states that in a triangle sum of the measures of angles is equal to 180°

m∠2 + m∠3 + m∠5 = 180°

Linear Pair:

The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.

m∠5 + m∠6 = 180°

For more explanation, refer the following link:

https://brainly.com/question/14256482

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