Question

complete the proofs below by filling in the missing statements and reasons. 10. given: ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary prove: ∠2≅∠3 statements reasons 1. ∠1 and ∠2 form a linear pair 1. given 2. ∠1 and ∠2 are supplementary 2. 3. m∠1 + m∠2 = 180° 3. 4. ∠1 and ∠3 are supplementary 4. 5. m∠1 + m∠3 = 180° 5. 6. m∠1 + m∠2 = m∠1 + m∠3 6. 7. m∠2 = m∠3 7. 8. ∠2≅∠3 8.

Explanation:

Step1: Define linear - pair property

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

Step2: Definition of supplementary angles

Supplementary angles have a sum of 180 degrees.

Step3: Given information

As stated in the problem.

Step4: Definition of supplementary angles

Same as step 2, since ∠1 and ∠3 are supplementary, their sum is 180 degrees.

Step5: Transitive property of equality

Since m∠1 + m∠2=180° and m∠1 + m∠3 = 180°, then m∠1 + m∠2=m∠1 + m∠3.

Step6: Subtraction property of equality

Subtract m∠1 from both sides of the equation m∠1 + m∠2=m∠1 + m∠3.

Step7: Definition of congruent angles

If two angles have the same measure, they are congruent.

Answer:

Statements	Reasons
2. ∠1 and ∠2 are supplementary	2. If two angles form a linear pair, they are supplementary
3. m∠1 + m∠2 = 180°	3. Definition of supplementary angles
4. ∠1 and ∠3 are supplementary	4. Given
5. m∠1 + m∠3 = 180°	5. Definition of supplementary angles
6. m∠1 + m∠2 = m∠1 + m∠3	6. Transitive property of equality
7. m∠2 = m∠3	7. Subtraction property of equality
8. ∠2 ≅ ∠3	8. Definition of congruent angles