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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:
    \[
    y^\circ = 180^\circ - (150^\circ + 30^\circ) = 180^\circ - 180^\circ = 0^\circ
    \]


### 

Find the value of x^0 in each of the following triangles (provided in the image).

Learn how to calculate the value of x° in different types of triangles using the Angle Sum Theorem and Exterior Angle Theorem. This step-by-step solution explains key geometric concepts and is suitable for students in Grades 7-9.

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