Question
se what you know about vertical angles to answer the question.(1 point)
In a geometric figure with 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?
In a geometric figure with 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?
Answers
GPT-4o mini
Vertical angles are angles that are opposite each other when two lines intersect. They are equal in measure. In this case, since ∠1 and ∠3 are vertical angles, we can set their measures equal to each other:
\[
m∠1 = m∠3
\]
Given that:
\[
m∠1 = (4x + 26)° \quad \text{and} \quad m∠3 = 98°
\]
Setting these equal, we have:
\[
4x + 26 = 98
\]
To solve for \(x\), first, subtract 26 from both sides:
\[
4x = 98 - 26
\]
\[
4x = 72
\]
Now, divide both sides by 4:
\[
x = \frac{72}{4} = 18
\]
Therefore, the value of \(x\) is \( \boxed{18} \).
\[
m∠1 = m∠3
\]
Given that:
\[
m∠1 = (4x + 26)° \quad \text{and} \quad m∠3 = 98°
\]
Setting these equal, we have:
\[
4x + 26 = 98
\]
To solve for \(x\), first, subtract 26 from both sides:
\[
4x = 98 - 26
\]
\[
4x = 72
\]
Now, divide both sides by 4:
\[
x = \frac{72}{4} = 18
\]
Therefore, the value of \(x\) is \( \boxed{18} \).