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Sagot :
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
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
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