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?(1 point)
Responses
3x°−75°=106°
3x°−75°+106°=90°
3x°−75°−106°=180°
3x°−75°+106°=180
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?(1 point)
Responses
68x°=2°
2x°+68°=180°
2x°=68°
x°=68°
The correct equation to solve for the value of each angle is:
∠1 + ∠3 = 68
chose from my answers
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.(1 point)
Responses
150°
90°
75°
120°
To solve for the measure of each angle, we need to divide the sum of the measures by 2 since vertical angles are congruent.
The correct answer is:
Each angle measures 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?(1 point)
Responses
14
18
72
98
To find the value of x, we can set the measure of ∠1 equal to the measure of ∠3, since they are a vertical pair.
Setting up the equation:
4x + 26 = 98
Now, we can solve for x.
4x = 98 - 26
4x = 72
x = 72/4
x = 18
So, the value of x is 18.
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
53°
6°
29°
15.3°
To find the measure of each angle, we can set the measure of ∠2 equal to the measure of ∠4, since they are a vertical pair.
Setting up the equation:
5x + 23 = 3x + 35
Now, we can solve for x.
5x - 3x = 35 - 23
2x = 12
x = 12/2
x = 6
To find the measure of each angle, we substitute the value of x back into the expressions:
∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53°
∠4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53°
So, the measure of each angle is 53°.