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Prove: [tex]\(m \angle C = 64\)[/tex]

Statement:
1. [tex]\( \triangle ABC \)[/tex] is a triangle.
2. [tex]\( m \angle A + m \angle B + m \angle C = 180 \)[/tex]
3. [tex]\( m \angle A = 3x + 8 \)[/tex]
4. [tex]\( m \angle B = 3x \)[/tex]
5. [tex]\( m \angle C = 3x + 10 \)[/tex]
6. [tex]\( 3x + 8 + 3x + 3x + 10 = 180 \)[/tex]
7. [tex]\( 9x + 18 = 180 \)[/tex]
8. [tex]\( 9x = 162 \)[/tex]
9. [tex]\( x = 18 \)[/tex]
10. [tex]\( m \angle C = 3(18) + 10 \)[/tex]
11. [tex]\( m \angle C = 64 \)[/tex]

Reason:
1. Given
2. Triangle Angle Sum Theorem
3. Given
4. Given
5. Given
6. Substitution
7. Algebra
8. Subtraction Property of Equality
9. Division Property of Equality
10. Substitution
11. Algebra

Select the reason that best supports Statement 10 in the given proof:
- Subtraction Property of Equality
- Division Property of Equality
- Substitution
- Symmetric Property



Answer :

GinnyAnswer
To prove that [tex]\(m \angle C = 64\)[/tex], we need to complete the steps provided and find the reason that best supports Statement 10 in the proof.

Let's go through the steps carefully:

1. Statement: [tex]\(\text{ABC is a triangle.}\)[/tex]
Reason: Given

2. Statement: [tex]\(m \angle A + m \angle B + m \angle C = 180\)[/tex]
Reason: Triangle Angle Theorem

3. Statement: [tex]\(m \angle A = 3x + 8\)[/tex]
Reason: Given

4. Statement: [tex]\(m \angle B = 3x\)[/tex]
Reason: Given

5. Statement: [tex]\(m \angle C = 3x + 10\)[/tex]
Reason: Given

6. Statement: [tex]\(3x + 8 + 3x + 3x + 10 = 180\)[/tex]
Reason: Substitution (Substituting the given values of [tex]\(m \angle A\)[/tex], [tex]\(m \angle B\)[/tex], and [tex]\(m \angle C\)[/tex] into the angle sum equation)

7. Statement: [tex]\(9x + 18 = 180\)[/tex]
Reason: Algebra (Combining like terms)

8. Statement: [tex]\(9x = 162\)[/tex]
Reason: Subtraction Property of Equality (Subtracting 18 from both sides)

9. Statement: [tex]\(x = 18\)[/tex]
Reason: Division Property of Equality (Dividing both sides by 9)

10. Statement: [tex]\(m \angle C = 3(18) + 10\)[/tex]
Reason: Substitution (Substituting [tex]\(x = 18\)[/tex] into the expression for [tex]\(m \angle C\)[/tex])

11. Statement: [tex]\(m \angle C = 64\)[/tex]
Reason: Algebra (Simplifying the expression)

Thus, in Statement 10, we substituted the value of [tex]\(x = 18\)[/tex] into the formula [tex]\(m \angle C = 3x + 10\)[/tex]. Therefore, the reason that best supports Statement 10 in the given proof is:

Substitution