Question

In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98° , what is the value of x ?(1 point)

Responses

7272

18
18

1414

98

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since ∠1 and ∠3 are a vertical pair, they are congruent angles and have equal measures.

Therefore, 4x + 26 = 98.

Subtracting 26 from both sides of the equation, we get:

4x = 98 - 26.

Simplifying the right side, we have:

4x = 72.

To solve for x, divide both sides of the equation by 4:

x = 72/4.

Simplifying the right side, we get:

x = 18.

Therefore, the value of x is 18.

Answer 2

Are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, I am sure. The value of x is 18.

Answer 4

For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)

Responses

15.3°15.3 degrees

6°6 degrees

29°29 degrees

53°

Answer 5

[AI-generated answer — Bot GPT 3.5]

Since vertical angles are congruent, ∠2 and ∠4 must have equal measures.

Therefore, we can set up the equation:

5x + 23 = 3x + 35.

Subtracting 3x from both sides of the equation, we get:

2x + 23 = 35.

Then, subtracting 23 from both sides, we have:

2x = 12.

Dividing both sides by 2, we get:

x = 6.

Now, we can find the measure of ∠2 and ∠4 by substituting the value of x:

∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.

∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.

Therefore, the measure of each angle is 53 degrees.

Answer 6

are you super sure?

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the incorrect response.

Let's find the correct measures of ∠2 and ∠4.

From the given information, we have:

m∠2 = (5x + 23)°

m∠4 = (3x + 35)°

Since ∠2 and ∠4 are vertical angles, they must have equal measures.

Therefore, we can set up the equation:

5x + 23 = 3x + 35.

Subtracting 3x from both sides, we get:

2x + 23 = 35.

Subtracting 23 from both sides, we have:

2x = 12.

Dividing both sides by 2, we get:

x = 6.

Now, let's substitute the value of x back into the expressions for ∠2 and ∠4:

m∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.

m∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.

Therefore, the measure of each angle is 53 degrees. I apologize again for the earlier confusion. I am sure that the correct measure for each angle is 53 degrees.

Answer 8

Thank you

Answer 9

[AI-generated answer — Bot GPT 3.5]

You're welcome! If you have any more questions, feel free to ask.