Question

How do I prove exterior angle theorem

Answer 1

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
StatementReason1ΔPQRΔPQR is a triangleGiven2m∠1+m∠2+m∠3=180°m∠1+m∠2+m∠3=180°Triangle Sum Theorem3∠3∠3 and ∠4∠4 form a linear pairDefinition of linear pair.4∠3∠3 and ∠4∠4 are supplementaryIf two angles form a linear pair, they are supplementary.5m∠3+m∠4=180°m∠3+m∠4=180°Definition of supplementary angles.6m∠3+m∠4=m∠1+m∠2+m∠3m∠3+m∠4=m∠1+m∠2+m∠3Statements 2, 5 and Substitution Property.7m∠4=m∠1+m∠2m∠4=m∠1+m∠2Subtraction Property.   im 99.9 perecent sure this is right bc im only in middle school but hope it helps