Selesaikan masalah berikut.

Let's solve these geometry problems step-by-step.

:

• Step 1: Identify the type of triangle. The markings on two sides of the triangle indicate that these sides are equal in length. This means it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal.

• Step 2: Find the interior angle adjacent to $x$. The angle opposite the side marked with two dashes is $50^\circ$. The angle opposite the other side marked with two dashes is the interior angle adjacent to $x$. Therefore, this interior angle is also $50^\circ$.

• Step 3: Calculate $x$. The angle $x$ and the interior angle $50^\circ$ form a linear pair (angles on a straight line). The sum of angles on a straight line is $180^\circ$.

  $$x + 50^\circ = 180^\circ$$ $$x = 180^\circ - 50^\circ$$ $$x = \boxed{\text{130}^\circ}$$

:

• Step 1: Find the interior angle at the bottom left vertex. The exterior angle at the bottom left vertex is $120^\circ$. The interior angle and this exterior angle form a linear pair.

  $$\text{Interior angle}_1 = 180^\circ - 120^\circ$$ $$\text{Interior angle}_1 = 60^\circ$$

• Step 2: Find the interior angle at the bottom right vertex. The exterior angle at the bottom right vertex is $75^\circ$. The interior angle and this exterior angle form a linear pair.

  $$\text{Interior angle}_2 = 180^\circ - 75^\circ$$ $$\text{Interior angle}_2 = 105^\circ$$

• Step 3: Calculate $x$. The sum of the interior angles in any triangle is $180^\circ$.

  $$x + \text{Interior angle}_1 + \text{Interior angle}_2 = 180^\circ$$ $$x + 60^\circ + 105^\circ = 180^\circ$$ $$x + 165^\circ = 180^\circ$$ $$x = 180^\circ - 165^\circ$$ $$x = \boxed{\text{15}^\circ}$$