Question

1. ∠2 and ∠dea are supplementary
2. m∠2 + m∠dea = 180°
3. m∠1 + m∠3 = m∠dea
4. m∠2 + m∠1 + m∠3 = 180°
5. m∠1 = m∠2
6. m∠2 + m∠2 + m∠3 = 180°
7. m∠3 = 110°
8. m∠2 + m∠2 + 110° = 180°
9. 2(m∠2) + 110° = 180°
10. 2(m∠2) = 70°
11. m∠2 = 35°

options:

1. given
2. def. of supp. ∠s
3. ∠ add. post.
4. subst. prop. of =
5. given
6. subst. prop. of =
7. given
8. subst. prop. of =
9. simplify
10. subt. prop. of =
11. div. prop. of =

options:

1. given
2. lin. pair thm.
3. ∠ add. post.
4. subst. prop. of =
5. vert. ∠s thm.
6. subst. prop. of =
7. given
8. subst. prop. of =
9. simplify
10. subt. prop. of =
11. div. prop. of =

options:

1. given
2. def. of supp. ∠s
3. ∠ add. post.
4. subst. prop. of =
5. given
6. ∠ add. post.
7. given
8. ∠ add. post.
9. simplify
10. add. prop. of =
11. mult. prop. of =

options:

1. given
2. def. of supp. ∠s
3. ∠ add. post.
4. subst. prop. of =
5. given
6. subst. prop. of =
7. given
8. subst. prop. of =
9. simplify
10. subt. prop. of =
11. mult. prop. of =

Explanation:

Step1: Identify given info

∠2 and ∠DBA are supplementary (Given)

Step2: Def. of supplementary angles

m∠2 + m∠DBA = 180° (Def. of Supp.)

Step3: Angle Addition Postulate

m∠1 + m∠3 = m∠DBA (Angle Add. Post.)

Step4: Substitute ∠DBA measure

m∠2 + m∠1 + m∠3 = 180° (Subst. Prop. of =)

Step5: Given angle equality

m∠1 = m∠2 (Given)

Step6: Substitute ∠1 with ∠2

m∠2 + m∠2 + m∠3 = 180° (Subst. Prop. of =)

Step7: Given ∠3 measure

m∠3 = 110° (Given)

Step8: Substitute ∠3 measure

m∠2 + m∠2 + 110° = 180° (Subst. Prop. of =)

Step9: Combine like terms

2(m∠2) + 110° = 180° (Simplify)

Step10: Subtract 110° from both sides

2(m∠2) = 70° (Subtraction Prop. of =)

Step11: Divide both sides by 2

m∠2 = 35° (Division Prop. of =)

Answer:

1. Given
2. Def. of Supp.
3. Angle Add. Post.
4. Subst. Prop. of =
5. Given
6. Subst. Prop. of =
7. Given
8. Subst. Prop. of =
9. Simplify
10. Subtraction Prop. of =
11. Division Prop. of =