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
7272
1414
18
Since angle ∠1 and angle ∠3 are vertical angles, they are congruent. Therefore, m∠1 = m∠3 = 98°.
We can set up an equation and solve for x:
4x + 26 = 98
Subtract 26 from both sides:
4x = 98 - 26
4x = 72
Divide both sides by 4:
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
53°
53 degrees
15.3°15.3 degrees
6°6 degrees
29°
Since angle ∠2 and angle ∠4 are vertical angles, they are congruent. Therefore, the measure of each angle is the same.
We can set up an equation and solve for x:
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 the value of x back into one of the angle measures:
m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53
Therefore, the measure of each angle is 53 degrees.