Question

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

7272

1414

18
18

98

Answer 1

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°
53 degrees

6°6 degrees

29°29 degrees

15.3°

Answer 2

Since angles 1 and 3 are a vertical pair, they are congruent. Therefore, we can set up the equation:

m∠1 = m∠3
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.

Answer 3

To determine the measure of each angle, we can set up the equation:

m∠2 = m∠4

5x + 23 = 3x + 35

Subtract 3x from both sides:

2x + 23 = 35

Subtract 23 from both sides:

2x = 12

Divide both sides by 2:

x = 6

Now we can substitute x = 6 into either angle to find the measures:

m∠2 = 5(6) + 23 = 53 degrees

m∠4 = 3(6) + 35 = 53 degrees

Therefore, the measure of each angle is 53 degrees.