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)

Question

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

Answer 1

2x°=68°

This equation solves for the value of each angle.

Answer 2

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°

Answer 3

90°

The measure of each angle is 90 degrees.

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

9898

18
18

1414

72

Answer 5

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.

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

29°29 degrees

6°6 degrees

53°

Answer 7

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.