Problem 12

Explanation

Consider the small triangle at the bottom. The sum of angles in a triangle is $180^\circ$. Given the top vertex angle is $100^\circ$. So, the sum of the two base angles is:

Next, consider the large triangle. Its base angles are $(x+y)$ and $(y+x)$. Since $x+y = 80^\circ$, both base angles of the large triangle are $80^\circ$. The sum of angles in the large triangle is $180^\circ$:

Thus, the value of $a$ is $20^\circ$.