Question

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

Explanation:

Step1: Identify isosceles triangles

The tick marks show that the upper triangle has two equal sides, so it is isosceles. The base angles of this triangle are equal. Let the base angle be $y$.

Step2: Calculate base angle of upper triangle

Using the triangle angle sum theorem ($180^\circ$ total):
$$y = \frac{180^\circ - 33^\circ}{2} = 73.5^\circ$$

Step3: Find exterior angle for lower triangle

The angle $y$ is an exterior angle to the lower isosceles triangle. The lower triangle also has two equal sides (tick marks), so its two base angles are equal. The exterior angle equals the sum of the two non-adjacent interior angles. Since the lower triangle's two equal angles are $x$ and $x$, we have:
$$y = x + x$$

Step4: Solve for $x$

Substitute $y=73.5^\circ$:
$$x = \frac{73.5^\circ}{2} = 36.75^\circ$$

Answer:

$36.75$