Aconjecture and the paragraph proof used to prove the conjecture are shown. given: angle 2 is congruent to angle 3. prove: angle 1 and angle 3 are supplementary. a horizontal line. two rays extend from upper region of the line diagonally down to the left and right and intersect the line forming interior angles labeled as 2 and 3 and an exterior angle labeled as 1. drag an expression or statement to each box to complete the proof. ∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by . therefore, m∠1+ = 180° by the definition of supplementary. it is given that ∠2≅ so m∠2=m∠3 by the . by substitution, m∠1+m∠3=180° , so ∠1 and ∠3 are supplementary by the definition of supplementary. angle congruence postulate linear pair postulate m∠2 m∠3 ∠3 ∠2

∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Linear Postulate theorem. Therefore, m∠1+m∠2 = 180° by the definition of supplementary. It is given that ∠2≅ ∠3, so m∠2=m∠3 by the Congruence Postulate theorem. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary.

Find the diagram to the question attached.

From the diagram given, we can see that m<1 and m<2 forms a linear pair i.e they are supplementary by the LINEAR POSTULATE THEOREM

Since the supplementary angles sum up to 180 degrees, hence:

m<1 + m<2 = 180 ............... 1

Also, the interior angles m<2 and m<3 are also equal according to the CONGRUENCE POSTULATE THEOREM i.e

m<2 = m<3 ......................... 2

Substitute equation 2 into 1, equation 1 becomes:

This shows that m<1 and m<3 are also supplementary

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∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the LINEAR PAIR POSTULATE . Therefore, m∠1 + m∠2 = 180° by the definition of supplementary. It is given that ∠2 ≅ ∠3 so m∠2 = m∠3 by the ANGLE CONGRUENCE POSTULATE . By substitution, m∠1 + m∠3 = 180°, so ∠1 and ∠3 are supplementary by the definition of supplementary.

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