Question

There is a pair of vertical angles whose measures are m∠1=106° and m∠2=(3x−75)° . What equation can you write to solve for x ?

3x° - 75° + 106° = 180°
3x° - 75° = 106°
3x° -75° - 106° = 180°
3x° - 75° + 106° = 90°

choose from the responses

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct equation to solve for x is:

3x - 75 = 106

Answer 2

Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. Their sum of their measures is equal to 68° . What equation solves for the value of each angle?

responses:

x° = 68°
68x° = 2°
2x° = 68°
2x° + 68° = 180°

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct equation to solve for the value of each angle is:

∠1 + ∠3 = 68°

Answer 4

Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. Their sum of their measures is equal to 68° . What equation solves for the value of each angle?

responses:

x° = 68°
68x° = 2°
2x° = 68°
2x° + 68° = 180°

choose from the responses

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct equation to solve for the value of each angle is:

∠1 + ∠3 = 68°

Answer 6

choose from the responses

Answer 7

[AI-generated answer — Bot GPT 3.5]

My apologies for the confusion. The correct equation to solve for the value of each angle is:

x° + (3x-68)° = 68°

Answer 8

The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.

120°
150°
90°
75°

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve for the measure of each angle, let's assume one angle is x°. Since vertical angles are congruent, the other angle will also be x°. The sum of their measures is given as 300°.

So, the equation becomes:

x + x = 300

Simplifying the equation:

2x = 300

Solving for x:

x = 150

Therefore, the measure of each angle is 150°.

The correct answer is 150°.

Answer 10

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 ?

72
18
14
98

Answer 11

[AI-generated answer — Bot GPT 3.5]

Since ∠1 and ∠3 are a vertical pair, they are congruent. Therefore, we can set up the equation:

4x + 26 = 98

To solve for x:

Subtract 26 from both sides:

4x = 98 - 26 = 72

Divide both sides by 4:

x = 72 / 4 = 18

The value of x is 18.

Therefore, the correct answer is x = 18.