Question

Question

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)
x=

Answer 1

Since angles $m\angle 1$ 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, we have:

$$2x+26=14$$

Now, we can solve for $x$. First, subtract 26 from both sides:

$$2x=14-26$$

This simplifies to:

$$2x=-12$$

Next, divide both sides by 2:

$$x=-6$$

Thus, the value of $x$ is:

$$\boxed{{\displaystyle -6}}$$