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?

Answer 1

To solve for \( x \), we start by recognizing that vertical angles are equal. Therefore, we have:

\[ m\angle 1 = m\angle 3 \]

From the problem, we know:

\[ m\angle 1 = (4x + 26)^\circ \] \[ m\angle 3 = 98^\circ \]

Setting these two expressions equal to each other gives us the equation:

\[ 4x + 26 = 98 \]

Now, we can solve for \( x \).

1. Subtract 26 from both sides:

\[ 4x = 98 - 26 \]

\[ 4x = 72 \]

2. Now, divide both sides by 4:

\[ x = \frac{72}{4} \]

\[ x = 18 \]

Thus, the value of \( x \) is

\[ \boxed{18} \]