Question

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?(1 point) Responses 2x°+68°=180° 2 x plus 68 degrees equals 180 degrees x°=68° x equals 68 degrees 2x°=68° 2 x equals 68 degrees 68x°=2°

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct equation that solves for the value of each angle is:

2x° + 68° = 180°

Answer 2

The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point) Responses 90° 90 degrees 75° 75 degrees 120° 120 degrees 150°

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's represent the measure of one of the angles as x°. Since vertical angles are congruent, the measure of the other angle is also x°.

The sum of the measures of two vertical angles is 300°, so we can set up the equation:

x° + x° = 300°

2x° = 300°

Now, we can solve for x by dividing both sides of the equation by 2:

x = 300° / 2

x = 150°

Therefore, each angle measures 150°.

Answer 4

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 18 18 9898 7272 14

Answer 5

[AI-generated answer — Bot GPT 3.5]

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

m∠1 = m∠3
4x + 26 = 98

Now, let's solve for x:

4x = 98 - 26
4x = 72
x = 72/4
x = 18

So, the value of x is 18.

Answer 6

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 7

[AI-generated answer — Bot GPT 3.5]

Since ∠2 and ∠4 are vertical angles, they are congruent angles.

Therefore, we can set up an equation:

m∠2 = m∠4

5x + 23 = 3x + 35

To solve for x, we can subtract 3x from both sides:

2x + 23 = 35

Next, we can subtract 23 from both sides:

2x = 12

Finally, we can divide both sides by 2 to solve for x:

x = 6

Now, we can substitute the value of x back into the expressions for ∠2 and ∠4 to find their measures:

m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53°

m∠4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53°

Therefore, the measure of each angle is 53°.