Question

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°
5x + 100 = 180

• 100 - 100

5x = 80
5x/5 = 80/5
x = 16
explain the mistake: not equal to 100 should be equal to 100
find the correct answer: 5x = 100
x = 20

1. find the value of x.

(3x)° 39°
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)°
6x + 2x + 8 = 180
8x = 180
8x/8 = 180/8
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: should be 180 not 90
find the correct answer: 133°

1. find the value of x.

115° (5x - 10)°
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 angles are vertical - angles, so they are equal. The 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 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 divide by 3: $x = \frac{51}{3}=17$.

Step5: Analyze problem 3

When combining like - terms, $6x+2x+8 = 180$ should be $8x+8 = 180$, not $16x = 180$.

Step6: Solve for x in problem 3

Subtract 8 from both sides: $8x=180 - 8 = 172$. Then divide by 8: $x=\frac{172}{8}=21.5$.

Step7: Analyze problem 4

The concept of supplementary angles is misused. Supplementary angles add up to $180^{\circ}$, not $90^{\circ}$.

Step8: Solve for the supplement in problem 4

$180-47 = 133^{\circ}$.

Step9: Analyze problem 5

The two angles are supplementary. The equation $115=5x - 10$ is set up correctly. But when adding 10 to both sides, there is no error in the solving process.

Answer:

1. $x = 20$
2. $x = 17$
3. $x = 21.5$
4. $133^{\circ}$
5. $x = 25$ (no error in solving process for the correct equation)