Question

solve for x

Explanation:

Step1: Find angle $y$ first

The sum of interior angles in a triangle is $180^\circ$.
$y = 180^\circ - 102^\circ - 12^\circ = 66^\circ$

Step2: Relate $x$ and $y$

$x$ and the $12^\circ$ angle form a linear pair? No, use exterior angle property: $x$ is equal to the sum of the two non-adjacent interior angles of the triangle.
$x = y + 102^\circ$
Substitute $y=66^\circ$: $x = 66^\circ + 102^\circ = 168^\circ$
Alternative: Linear pair with the $12^\circ$ angle's adjacent interior angle: $x = 180^\circ - 12^\circ = 168^\circ$ (simpler, using linear pair and triangle exterior angle theorem)

Answer:

$168^\circ$