I've been stuck on this problem forever now! provide reasons for the proof. given: angle 2=4 and 2 and 3 are supplementary prove: angle 1=3 statement: reason 1. 2=4 1. given 2. m2=m4 2. angle congruence postulate 3. angles 2 and 3 are supplementary 3. given 4. m2+m3=180 4. definition of supplementary angles 5. angles 1 and 4 are supplementary 5. fill in blank 6. m1+m4=180 6. definition of supplementary angles 7. m1+m4=m2+m3 7. fill in blank 8. m1+m4=m4+m3 8. fill in blank 9. m1=m3 9. fill in blank 10. 1=3 10. fill in blank

Statement 1: ∠2=∠4 .. Given

Statement 2: Measure of angle 2 = Measure of angle 4 = Alternate angles

Statement 3: ∠2=∠3 , Given Supplementary Angles

Statement 4 : ∠2+∠3=180 , Sum of supplementary angles is equal to 180 degree.

Statement 5: ∠1 and ∠4 are supplementary angles because angle of a straight line is equal to 180 degree.

Statement 6: Measure of angle 1 + measure of angle 4 = 180, sum of angles of supplementary angles is 180 degree.

Statement 7:  ∠1+∠4= ∠2+∠3 ... Both sums are 180 degrees.

Statement 8: ∠1+∠4=∠4+∠3 .. ∠2 and ∠4 are equal (alternate angles)

Statement 9: ∠1= ∠3 , because ∠4 is common on both sides.

Statement 10: ∠1 = ∠3 .. hence, proved

Definitions, postulates, and theorems are defined relationships, between the angles, that are used to determine the values of the angles

The two column proof is presented as follows;

Statement                                      Reason

1. 2 = 4                                             1. Given

2. m∠2 = m∠4                                 2. Angle congruence postulate

3. ∠2 and ∠ 3 are supp ∠s             3. Given

4. m∠2 + m∠3 = 180°                       4. Definition Supplementary angles

5. ∠1 and 4 are supplementary      5. Linear pair angles theorem

6. m∠1 + m∠4 = 180°                        6. Definition of supplementary angles

7. m∠1 + m∠4 = m∠2 + m∠3           7. Transitive property of equality

8. m∠1 + m∠4 = m∠4 + m∠3           8. Transitive property of equality

9. m∠1 = m∠3                                   9. Addition property of equality

10. m∠1 = m∠3                                 10. Definition of equality

Reasons:

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it will be a cylinder. with a diameter of 8 and 4 single pieces high

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answer: about 22.67

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