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 = 180

• 100 - 100

5x = 80
5x/5 = 80/5
x = 16
explain the mistake: the mistake was they added both angles to 180° which is supplementary.
find the correct answer: vertical angles (5x) = 100° x = 20°

1. find the value of x.

3x + 39 = 180

• 39 - 39

3x = 141
3x/3 = 141/3
x = 47
explain the mistake: they thought it was supplementary but the correct relationship is they are complementary
find the cofrect answer:

1. find the value of x.

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:
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:

2. Find the value of \(x\).

Step1: Analyze the angle relationship

The given angle is a right - angle (\(90^{\circ}\)). The two angles \((3x)^{\circ}\) and \(39^{\circ}\) are complementary (their sum is \(90^{\circ}\)), not supplementary (\(180^{\circ}\)). The correct equation should be \(3x+39 = 90\).

Step2: Solve the correct equation

Subtract \(39\) from both sides of the equation \(3x+39 = 90\):
\(3x=90 - 39\)
\(3x = 51\)
Divide both sides by \(3\):
\(x=\frac{51}{3}=17\)

Step1: Analyze the error in combining like terms

In the original work, when combining \(6x+2x + 8=180\), the error was that \(8\) was ignored when combining like terms. The correct combination is \(6x+2x=8x\), and the equation should be \(8x+8 = 180\).

Step2: Solve the correct equation

Subtract \(8\) from both sides of \(8x+8 = 180\):
\(8x=180 - 8\)
\(8x = 172\)
Divide both sides by \(8\):
\(x=\frac{172}{8}=21.5\)

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\), not \(90^{\circ}\) (which is for complementary angles). The correct formula is \(180 - 47\).

Step2: Calculate the supplement

\(180-47 = 133^{\circ}\)

Answer:

\(x = 17\)

3. Find the value of \(x\).