Find the missing angles x, y, and k in the given triangles.

$$
x = 180^\circ - 130^\circ
$$
$$
x = 50^\circ
$$
The value of $x$ is $\boxed{\text{50}^\circ}$.

2. : The markings indicate that it is an isosceles triangle, meaning the two base angles are equal. One base angle is $50^\circ$, so the other base angle is also $50^\circ$. The sum of angles in a triangle is $180^\circ$.

$$
y = 180^\circ - 100^\circ
$$
$$
y = 80^\circ
$$
The value of $y$ is $\boxed{\text{80}^\circ}$.

3. : The markings indicate that all three sides of the triangle are equal, making it an equilateral triangle. All angles in an equilateral triangle are equal. The sum of angles in a triangle is $180^\circ$.

$$
k = 60^\circ
$$
The value of $k$ is $\boxed{\text{60}^\circ}$.

4. : The markings indicate that two sides of the triangle are equal, making it an isosceles triangle. The angles opposite the equal sides are equal.

$$
a = \frac{62^\circ}{2}
$$
$$
a = 31^\circ
$$
The value of $a$ is $\boxed{\text{31}^\circ}$.

5. : The markings indicate that sides AB and AC are equal, making it an isosceles triangle. The exterior angle at B is $108^\circ$.

Angles on a straight line sum to $180^\circ$. $\angle ABC = 180^\circ - 108^\circ = 72^\circ$

Set up the equation for the sum of angles. $y + 72^\circ + 72^\circ = 180^\circ$

$$
y + 144^\circ = 180^\circ
$$
$$
y = 180^\circ - 144^\circ
$$
$$
y = 36^\circ
$$
The value of $y$ is $\boxed{\text{36}^\circ}$.

6. : The triangle is a right-angled triangle, so one angle is $90^\circ$. The sum of angles in a triangle is $180^\circ$.