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
x°=68°
x equals 68 degrees
68x°=2°
68 x equals 2
2x°=68°
2 x equals 68 degrees
2x°+68°=180° 2 x plus 68 degrees equals 180 degrees
2x°=68°
This equation solves for the value of each angle.
The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point)
Responses
75°
75 degrees
120°
120 degrees
150°
150 degrees
90°
90°
The measure of each angle is 90 degrees.
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
9898
18
18
1414
72
From the given information, we know that ∠1 and ∠3 are a vertical pair. This means that their measures are equal.
So, we have:
m∠1 = m∠3
4x + 26 = 98
Now, we can solve for x:
4x = 98 - 26
4x = 72
x = 72/4
x = 18
Therefore, 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
15.3°15.3 degrees
29°29 degrees
6°6 degrees
53°
Two vertical angles have the same measure.
We have m∠2 = m∠4,
so we can set up the equation:
5x + 23 = 3x + 35
Now let's solve for x:
5x - 3x = 35 - 23
2x = 12
x = 12/2
x = 6
Now we can find the measure of each angle by substituting the value of x back into their respective expressions:
m∠2 = 5x + 23
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53
m∠4 = 3x + 35
m∠4 = 3(6) + 35
m∠4 = 18 + 35
m∠4 = 53
Therefore, the measure of each angle is 53 degrees.