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

Answer 1

Vertical angles are equal, so we have:

\[ m∠1 = m∠3 \]

Given that \( m∠1 = (2x + 26)° \) and \( m∠3 = 14° \), we can set up the equation:

\[ 2x + 26 = 14 \]

Now, let's solve for \( x \).

1. Subtract 26 from both sides:

\[ 2x = 14 - 26 \]

\[ 2x = -12 \]

2. Divide both sides by 2:

\[ x = -\frac{12}{2} \]

\[ x = -6 \]

Thus, the value of \( x \) is:

\[ \boxed{-6} \]