Question

prove exterior angle property​

Answer 1

Answer:

Exterior Angle Theorem

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∠2

Proof:

Given: ΔPQR

To Prove: m∠4=m∠1+m∠2

Statement

Reason

1

ΔPQR is a triangle

Given

2

m∠1+m∠2+m∠3=180°

Triangle Sum Theorem

3

∠3 and ∠4 form a linear pair

Definition of linear pair.

4

∠3 and ∠4 are supplementary

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

5

m∠3+m∠4=180°

Definition of supplementary angles.

6

m∠3+m∠4=m∠1+m∠2+m∠3

Statements 2, 5 and Substitution Property.

7

m∠4=m∠1+m∠2

Subtraction Property.

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