Question

find the value of x.
if necessary, you may learn what the markings on a figure indicate.

Explanation:

Step1: Identify equal side segments

The tick marks show:

• The left segment of the top side = the middle segment of the top side
• The middle segment of the bottom side = the right side of the figure

So, the triangle on the left is isosceles, and the figure on the right is a parallelogram.

Step2: Calculate base angle of left triangle

For the left isosceles triangle, the base angles are equal. The vertex angle is $30^\circ$, so each base angle is:
$\frac{180^\circ - 30^\circ}{2} = 75^\circ$

Step3: Find adjacent angle to base angle

The supplementary angle to $75^\circ$ (since they form a straight line) is:
$180^\circ - 75^\circ = 105^\circ$

Step4: Use parallelogram angle property

In a parallelogram, opposite angles are equal. The angle we found ($105^\circ$) is opposite to $x$, so $x = 105^\circ$.

Answer:

$105^\circ$