Question

what is the value of angle x in the figure below?

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle opposite to the $51^{\circ}$ angle is also $51^{\circ}$.

Step2: Use angle - sum property of a right - angle

The right - angle formed by $CD$ and $EF$ is $90^{\circ}$. Let the unknown angle $x$. We know that the sum of the angle adjacent to $x$ (which is equal to $51^{\circ}$) and $x$ is $90^{\circ}$. So, $x + 51^{\circ}=90^{\circ}$.

Step3: Solve for $x$

Subtract $51^{\circ}$ from both sides of the equation $x + 51^{\circ}=90^{\circ}$. We get $x=90^{\circ}-51^{\circ}$.
$x = 39^{\circ}$

Answer:

$39^{\circ}$