Question

find the value of x. x =

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle measuring $45^{\circ}$ and the angle measuring $5(x + 7)^{\circ}$ are vertical angles. So, we can set up an equation based on the property of vertical - angles.
$5(x + 7)=45$

Step2: Expand the left - hand side

Using the distributive property $a(b + c)=ab+ac$, we have $5x+35 = 45$.
$5x+35=45$

Step3: Isolate the variable term

Subtract 35 from both sides of the equation:
$5x+35 - 35=45 - 35$
$5x=10$

Step4: Solve for x

Divide both sides of the equation by 5:
$\frac{5x}{5}=\frac{10}{5}$
$x = 2$

Answer:

$2$