Angles m∠1 and m∠3 are vertical angles. If m∠1=(2x+26)° and m∠3=14° , what is the value of x ?(1 point)

Question

x= ___

Answer 1

Since \( m\angle 1 \) and \( m\angle 3 \) are vertical angles, they are equal. Therefore, we can set up the equation:

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

Substituting the given expressions:

\[ (2x + 26) = 14 \]

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

1. Subtract 26 from both sides:

\[ 2x = 14 - 26 \]

\[ 2x = -12 \]

2. Divide both sides by 2:

\[ x = -6 \]

Thus, the value of \( x \) is \( \boxed{-6} \).