The correct equation to solve for x is: 3x° − 75° = 106°.
Vertical angles are formed when two lines intersect. They are opposite angles and have equal measures. In this problem, angle 1 and angle 2 are vertical angles and have the same measure.
The measure of angle 1 is given as 106°. The measure of angle 2 is represented as (3x − 75)°. Since these angles are equal, we can set up the equation:
m∠1 = m∠2
106° = (3x − 75)°
Simplifying the equation gives:
3x − 75 = 106
Solving for x, we add 75 to both sides of the equation:
3x = 106 + 75
3x = 181
Finally, dividing both sides of the equation by 3 gives:
x = 181 / 3
So, the correct equation to solve for x is 3x° − 75° = 106°.
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?
Responses
3x° − 75° = 106°
3x° − 75° + 106° = 90°
3x°−75°+106° = 180°
3x° − 75° − 106° = 180°
Explain
11 answers
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°
2x° + 68° = 180°
68x° = 2°
2x° = 68°
Responses
x° = 68°
2x° + 68° = 180°
68x° = 2°
2x° = 68°
The correct equation to solve for the value of each angle is: 2x° + 68° = 180°.
Vertical angles are opposite angles formed by intersecting lines. In this problem, angles ∠1 and ∠3 are a vertical pair, and their measures add up to 68°.
We can set up the equation:
∠1 + ∠3 = 68°
Since angles ∠1 and ∠3 are vertical angles, they have the same measure. We can represent the measure of angle ∠1 as x° and the measure of angle ∠3 as x°.
Substituting these values into the equation gives us:
x° + x° = 68°
Simplifying the equation gives:
2x° = 68°
To solve for x, we divide both sides of the equation by 2:
x° = 68° / 2
Therefore, the correct equation to solve for the value of each angle is 2x° + 68° = 180°.
Vertical angles are opposite angles formed by intersecting lines. In this problem, angles ∠1 and ∠3 are a vertical pair, and their measures add up to 68°.
We can set up the equation:
∠1 + ∠3 = 68°
Since angles ∠1 and ∠3 are vertical angles, they have the same measure. We can represent the measure of angle ∠1 as x° and the measure of angle ∠3 as x°.
Substituting these values into the equation gives us:
x° + x° = 68°
Simplifying the equation gives:
2x° = 68°
To solve for x, we divide both sides of the equation by 2:
x° = 68° / 2
Therefore, the correct equation to solve for the value of each angle is 2x° + 68° = 180°.
The sum of the measures of two vertical angles is 300°. Solve for the measure of each angle.
Responses
90°
150°
120°
75°
Responses
90°
150°
120°
75°
To solve for the measure of each angle, let's assume that the first angle is x°. Since vertical angles are equal, the second angle will also be x°.
The sum of the measures of two vertical angles is 300°, so we can write the equation:
x + x = 300
Simplifying the equation gives:
2x = 300
Dividing both sides of the equation by 2 gives:
x = 150
Therefore, each angle measures 150°.
The correct answer is 150°.
The sum of the measures of two vertical angles is 300°, so we can write the equation:
x + x = 300
Simplifying the equation gives:
2x = 300
Dividing both sides of the equation by 2 gives:
x = 150
Therefore, each angle measures 150°.
The correct answer is 150°.
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?
Responses
72
14
18
98
Responses
72
14
18
98
To find the value of x, we use the fact that vertical angles are equal.
Given that ∠1 and ∠3 are a vertical pair, and m∠1 = (4x + 26)° and m∠3 = 98°, we can set up the equation:
(4x + 26)° = 98°
To solve for x, we subtract 26 from both sides of the equation:
4x = 98° - 26°
4x = 72
Finally, we divide both sides of the equation by 4:
x = 72 / 4
Therefore, the value of x is 18.
The correct answer is 18.
Given that ∠1 and ∠3 are a vertical pair, and m∠1 = (4x + 26)° and m∠3 = 98°, we can set up the equation:
(4x + 26)° = 98°
To solve for x, we subtract 26 from both sides of the equation:
4x = 98° - 26°
4x = 72
Finally, we divide both sides of the equation by 4:
x = 72 / 4
Therefore, the value of x is 18.
The correct answer is 18.
For two vertical angles with measures m∠2 = (5x + 23)° and m∠4 = (3x + 35)°, what is the measure of each angle?
Responses
6°
53°
15.3°
29°
Responses
6°
53°
15.3°
29°
To find the measure of each angle, we use the fact that vertical angles are equal.
Given that ∠2 and ∠4 are a vertical pair, and m∠2 = (5x + 23)° and m∠4 = (3x + 35)°, we can set up the equation:
(5x + 23)° = (3x + 35)°
To solve for x, we subtract 3x from both sides of the equation and subtract 23 from both sides:
5x - 3x = 35° - 23°
2x = 12
Finally, we divide both sides of the equation by 2:
x = 12 / 2
Therefore, the value of x is 6.
To find the measure of each angle, we substitute x = 6 into the given expressions for ∠2 and ∠4:
m∠2 = (5x + 23)° = (5*6 + 23)° = 53°
m∠4 = (3x + 35)° = (3*6 + 35)° = 53°
Therefore, the measure of each angle is 53°.
The correct answer is 53°.
Given that ∠2 and ∠4 are a vertical pair, and m∠2 = (5x + 23)° and m∠4 = (3x + 35)°, we can set up the equation:
(5x + 23)° = (3x + 35)°
To solve for x, we subtract 3x from both sides of the equation and subtract 23 from both sides:
5x - 3x = 35° - 23°
2x = 12
Finally, we divide both sides of the equation by 2:
x = 12 / 2
Therefore, the value of x is 6.
To find the measure of each angle, we substitute x = 6 into the given expressions for ∠2 and ∠4:
m∠2 = (5x + 23)° = (5*6 + 23)° = 53°
m∠4 = (3x + 35)° = (3*6 + 35)° = 53°
Therefore, the measure of each angle is 53°.
The correct answer is 53°.
are you sure
Apologies for the confusion caused. Let's reevaluate the problem.
Given that ∠2 has a measure of (5x + 23)° and ∠4 has a measure of (3x + 35)°, we can set up the equation:
m∠2 = m∠4
(5x + 23)° = (3x + 35)°
To solve for x, we'll simplify the equation:
5x + 23 = 3x + 35
Next, we'll subtract 3x from both sides:
5x - 3x + 23 = 3x - 3x + 35
This simplifies to:
2x + 23 = 35
Then, we'll subtract 23 from both sides:
2x + 23 - 23 = 35 - 23
Which gives us:
2x = 12
Finally, we'll divide both sides by 2:
2x/2 = 12/2
x = 6
Now, substituting the value of x back into either ∠2 or ∠4, let's find the measure of each angle:
m∠2 = (5x + 23)° = (5*6 + 23)° = 53°
m∠4 = (3x + 35)° = (3*6 + 35)° = 53°
Therefore, the measure of each angle is indeed 53°.
I apologize for any confusion earlier, and the correct response is indeed 53°.
Given that ∠2 has a measure of (5x + 23)° and ∠4 has a measure of (3x + 35)°, we can set up the equation:
m∠2 = m∠4
(5x + 23)° = (3x + 35)°
To solve for x, we'll simplify the equation:
5x + 23 = 3x + 35
Next, we'll subtract 3x from both sides:
5x - 3x + 23 = 3x - 3x + 35
This simplifies to:
2x + 23 = 35
Then, we'll subtract 23 from both sides:
2x + 23 - 23 = 35 - 23
Which gives us:
2x = 12
Finally, we'll divide both sides by 2:
2x/2 = 12/2
x = 6
Now, substituting the value of x back into either ∠2 or ∠4, let's find the measure of each angle:
m∠2 = (5x + 23)° = (5*6 + 23)° = 53°
m∠4 = (3x + 35)° = (3*6 + 35)° = 53°
Therefore, the measure of each angle is indeed 53°.
I apologize for any confusion earlier, and the correct response is indeed 53°.
1 answer