Set up equations and solve them to find the unknown number in the following case:

The sum of $5$ times a number and $6$ is $15$.

Set up equations and solve them to find the unknown number in the following case:

If $\frac{3}{5}$ times a number taken away from $16$, the result is the number itself, what is the number.

Ibenhal thinks of a number. If she adds $19$ to it and divides the sum by $5$, she will get $8$. Find the unknown number.

Set up equations and solve them to find the unknown number in the following case:

When $6$ subtracted from thrice a number, the result is $9$. Find the number. 

In an isosceles triangle, the base angles are equal. The vertex angle is $40°$. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is $180°$). 

If the base angles of a triangle are $b=k°$, write $k$ as the final answer.