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.
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
3 answers
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°
Responses
53°
53 degrees
6°6 degrees
29°29 degrees
15.3°
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.
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.