Question

solve for x. (4x + 38)° 118° x =

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle $(4x + 38)^{\circ}$ and the angle adjacent to the $118^{\circ}$ angle are vertical - angles. The angle adjacent to the $118^{\circ}$ angle is $180 - 118=62^{\circ}$ (since they are linear - pair angles and linear - pair angles add up to $180^{\circ}$).

Step2: Set up the equation

Since vertical angles are equal, we set up the equation $4x+38 = 62$.

Step3: Solve the equation for x

Subtract 38 from both sides: $4x=62 - 38$. So, $4x = 24$. Then divide both sides by 4: $x=\frac{24}{4}=6$.

Answer:

$6$