Question

angle relationships error analysis
each of the problems below was solved incorrectly. for each problem, circle the mistake in the work/answer, explain what the mistake is, and find the correct answer.

1. find the value of x.

5x + 100 = 180

• 100 - 100

5x = 80
5x/5 = 80/5
x = 16
explain the mistake:
find the correct answer:

1. find the value of x.

3x + 39 = 180

• 39 - 39

3x = 141
3x/3 = 141/3
x = 47
explain the mistake:
find the correct answer:

1. find the value of x.

6x + 2x + 8 = 180
8x = 180
8x/16 = 180/16
x = 11.25
explain the mistake:
find the correct answer:

1. an angle measures 47°. what is the measure of its supplement?

90 - 47 = 43°
explain the mistake:
find the correct answer:

1. find the value of x.

115 = 5x - 10
+ 10 + 10
125 = 5x
125/5 = 5x/5
x = 25
explain the mistake:
find the correct answer:

Explanation:

Step1: Analyze problem 1

The two angles are vertical - angles and should be equal, not supplementary. The correct equation should be $5x = 100$, not $5x+100 = 180$.

Step2: Solve for $x$ in problem 1

Divide both sides of $5x = 100$ by 5: $x=\frac{100}{5}=20$.

Step3: Analyze problem 2

The two angles are complementary, not supplementary. The correct equation should be $3x + 39=90$, not $3x + 39 = 180$.

Step4: Solve for $x$ in problem 2

Subtract 39 from both sides: $3x=90 - 39=51$, then $x = 17$.

Step5: Analyze problem 3

The two angles are supplementary, but there is a calculation error when combining like - terms. It should be $6x+2x + 8=180$, i.e., $8x+8 = 180$, not $16x = 180$.

Step6: Solve for $x$ in problem 3

First, subtract 8 from both sides: $8x=180 - 8 = 172$, then $x=\frac{172}{8}=21.5$.

Step7: Analyze problem 4

The concept of supplementary angles is misused. Supplementary angles add up to $180^{\circ}$, not $90^{\circ}$. The correct calculation is $180-47 = 133^{\circ}$.

Step8: Analyze problem 5

The two angles are supplementary, but there is a sign - error in setting up the equation. It should be $115+(5x - 10)=180$, not $115 = 5x-10$.

Step9: Solve for $x$ in problem 5

First, simplify the left - hand side: $115+5x-10 = 180$, i.e., $5x+105 = 180$. Then subtract 105 from both sides: $5x=180 - 105 = 75$, and $x = 15$.

Answer:

1. Mistake: Incorrectly assumed vertical angles are supplementary. Correct answer: $x = 20$.
2. Mistake: Incorrectly assumed complementary angles are supplementary. Correct answer: $x = 17$.
3. Mistake: Incorrect combination of like - terms. Correct answer: $x = 21.5$.
4. Mistake: Misused the concept of supplementary angles. Correct answer: $133^{\circ}$.
5. Mistake: Incorrect equation - setting due to sign error. Correct answer: $x = 15$.