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

Answer 1

Since vertical angles are congruent, the measure of the vertical angle must be equal to 106°:

3x - 75 = 106

Answer 2

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

Answer 3

To solve for the value of each angle, let's assume that the measures of ∠1 and ∠3 are x and y, respectively.

Since ∠1 and ∠3 form a vertical pair, they are congruent. Therefore, their measures are equal:

x = y

The sum of their measures is equal to 68°:

x + y = 68

Using the equation x = y, we can rewrite the equation as:

x + x = 68
2x = 68
x = 34

Therefore, the measure of ∠1 is 34° and the measure of ∠3 is also 34°.

Answer 4

wrong

Answer 5

Apologies for the mistake. Let's correct it.

Let's assume that the measures of ∠1 and ∠3 are x and y, respectively.

Since vertical angles are congruent, we have:

x = y

The sum of the measures of vertical angles is equal to 68°:

x + y = 68

Substituting y with x in the second equation, we get:

x + x = 68
2x = 68
x = 34

Therefore, the measure of ∠1 is 34° and the measure of ∠3 is also 34°.

Answer 6

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

Answer 7

Since ∠1 and ∠3 are a vertical pair, they are congruent. Therefore, we have:

m∠1 = m∠3

Given that m∠1 = (4x + 26)° and m∠3 = 98°, we can set up the equation:

(4x + 26)° = 98°

Now, we can solve for x by subtracting 26 from both sides of the equation:

4x = 98 - 26 = 72

Finally, divide both sides of the equation by 4 to solve for x:

x = 72/4 = 18

Therefore, the value of x is 18.

Answer 8

For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle

Answer 9

Since vertical angles are congruent, the measure of ∠2 is equal to the measure of ∠4:

m∠2 = m∠4

Given that m∠2 = (5x + 23)° and m∠4 = (3x + 35)°, we can set up the equation:

5x + 23 = 3x + 35

Now, let's solve for x. First, subtract 3x from both sides of the equation:

5x - 3x + 23 = 3x - 3x + 35

2x + 23 = 35

Next, subtract 23 from both sides of the equation:

2x + 23 - 23 = 35 - 23

2x = 12

Finally, divide both sides of the equation by 2 to solve for x:

2x/2 = 12/2

x = 6

Now, substitute the value of x back into either equation to find the measure of ∠2 or ∠4. Let's use ∠2:

m∠2 = (5x + 23)°
m∠2 = (5 * 6 + 23)°
m∠2 = (30 + 23)°
m∠2 = 53°

Therefore, the measure of ∠2 is 53° and the measure of ∠4 is also 53°.