Let's analyze the three triangles to find the value of $x^\circ$ for each.

a) Triangle a:

• This is a standard triangle with all three angles labeled. The known angles are $42^\circ$ and $72^\circ$.
• Since the sum of the angles in a triangle is always $180^\circ$, we can find $x^\circ$ by: $x^\circ = 180^\circ - (42^\circ + 72^\circ) = 180^\circ - 114^\circ = 66^\circ$ Therefore, $x^\circ = 66^\circ$.

b) Triangle b:

• This triangle has an external angle labeled as $150^\circ$.
• The external angle of a triangle is equal to the sum of the two opposite interior angles. In this case, $x^\circ$ is one of those opposite angles. Let $y^\circ$ be the other interior angle.
• The equation for the external angle is: $150^\circ = x^\circ + y^\circ$
  • There is a $30^\circ$ angle inside the triangle. Since the sum of angles in a triangle is $180^\circ$, the third angle $y^\circ$ can be calculated: $y^\circ = 180^\circ - (150^\circ + 30^\circ) = 180^\circ - 180^\circ = 0^\circ$