A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angl
e 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°
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°
2 answers:
Answer:
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
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