Question
Use what you know about vertical angles to answer the questions. In geometric figures 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? A:98 B: 14 C: 72 D: 18
Answers
GPT-4o mini
In a pair of vertical angles, the angles are equal. Since ∠1 and ∠3 are a vertical pair, we can set their measures equal to each other:
\[
m \angle 1 = m \angle 3
\]
Given:
\[
m \angle 1 = 4x + 26
\]
\[
m \angle 3 = 98
\]
Setting them equal:
\[
4x + 26 = 98
\]
To solve for \(x\), subtract 26 from both sides:
\[
4x = 98 - 26
\]
\[
4x = 72
\]
Now, divide both sides by 4:
\[
x = \frac{72}{4} = 18
\]
Thus, the value of \(x\) is \( \boxed{18} \).
\[
m \angle 1 = m \angle 3
\]
Given:
\[
m \angle 1 = 4x + 26
\]
\[
m \angle 3 = 98
\]
Setting them equal:
\[
4x + 26 = 98
\]
To solve for \(x\), subtract 26 from both sides:
\[
4x = 98 - 26
\]
\[
4x = 72
\]
Now, divide both sides by 4:
\[
x = \frac{72}{4} = 18
\]
Thus, the value of \(x\) is \( \boxed{18} \).