Question

state and prove that the exterior angle theorem​

Answer 1

hola mate .... here is ur answer :)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.



m∠4=m∠1+m∠2m∠4=m∠1+m∠2

Proof:

Given: ΔPQRΔPQR

To Prove: m∠4=m∠1+m∠2m∠4=m∠1+m∠2

Statement

Reason

1

ΔPQRΔPQR is a triangle

Given

2

m∠1+m∠2+m∠3=180°m∠1+m∠2+m∠3=180°

Triangle Sum Theorem

3

∠3∠3 and ∠4∠4 form a linear pair

Definition of linear pair.

4

∠3∠3 and ∠4∠4 are supplementary

If two angles form a linear pair, they are supplementary.

5

m∠3+m∠4=180°m∠3+m∠4=180°

Definition of supplementary angles.

6

m∠3+m∠4=m∠1+m∠2+m∠3m∠3+m∠4=m∠1+m∠2+m∠3

Statements 2, 5 and Substitution Property.

7

m∠4=m∠1+m∠2

hope it helps :)

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Answer 2

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.



m∠4=m∠1+m∠2m∠4=m∠1+m∠2

Proof:

Given: ΔPQRΔPQR

To Prove: m∠4=m∠1+m∠2m∠4=m∠1+m∠2

Statement

Reason

1

ΔPQRΔPQR is a triangle

Given

2

m∠1+m∠2+m∠3=180°m∠1+m∠2+m∠3=180°

Triangle Sum Theorem

3

∠3∠3 and ∠4∠4 form a linear pair

Definition of linear pair.

4

∠3∠3 and ∠4∠4 are supplementary

If two angles form a linear pair, they are supplementary.

5

m∠3+m∠4=180°m∠3+m∠4=180°

Definition of supplementary angles.

6

m∠3+m∠4=m∠1+m∠2+m∠3m∠3+m∠4=m∠1+m∠2+m∠3

Statements 2, 5 and Substitution Property.

7

m∠4=m∠1+m∠2

hope it helps :)