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
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°.
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°
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°
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°.
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
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.
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°
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°.