Atriangle 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°

The Three options are

1.  m∠5 + m∠6 = 180°  ...........Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Step-by-step explanation:

Consider Δ ABC with Exterior angles as

∠ 1 , ∠ 4 ,and ∠ 6

Exterior angle Property of Triangle:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠ 1 we have

∠ 1 = ∠ 5 + ∠ 3 .................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 4 we have

∠ 4 = ∠ 5 + ∠ 2.................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 6 we have

∠ 6 = ∠ 2 + ∠ 3.................Exterior angle Property of Triangle

Triangle Sum Property:

Ina triangle sum of the measures of angles is equal to 180°

∴ m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Linear Pair:

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

∴ m∠5 + m∠6 = 180°  ...........Linear Pair

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc