Question

find the value of $x$. the figure shows intersecting lines with angles marked as $35^\circ$ and $94^\circ$.

Explanation:

Step1: Find alternate interior angle

The angle alternate to the 35° angle is also $35^\circ$.

Step2: Use angle sum in triangle

The three angles (35°, $x$, supplementary of 94°) sum to $180^\circ$. First calculate the supplementary angle: $180^\circ - 94^\circ = 86^\circ$.

Step3: Solve for $x$

Set up the equation: $x + 35^\circ + 86^\circ = 180^\circ$. Simplify: $x = 180^\circ - 35^\circ - 86^\circ$

Answer:

$59^\circ$