Question

find the value of x.

x =

Explanation:

Step1: Identify angle - relationship

Since $\angle AFB$ and $\angle DFC$ are vertical angles, $\angle AFB=\angle DFC$. Also, $\angle AFE = 90^{\circ}$, and $\angle AFB = 37^{\circ}$, so $\angle BFE=90^{\circ}-37^{\circ}=53^{\circ}$. And $\angle BFE$ and $\angle DFC=(2x + 3)^{\circ}$ are vertical - angles, so $(2x + 3)^{\circ}=53^{\circ}$.

Step2: Solve the equation for x

We have the equation $2x+3 = 53$. First, subtract 3 from both sides: $2x=53 - 3$. So $2x=50$. Then divide both sides by 2: $x=\frac{50}{2}$.

Answer:

$x = 25$