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The given problem involves a triangle where an exterior angle of 153° is formed, and you need to find the value of \(x^\circ\), which is one of the interior angles of the triangle.

### Steps to solve:

1. The triangle shown is a right triangle, as indicated by the right angle (90°).
2. The exterior angle theorem states that the exterior angle (153°) is equal to the sum of the two non-adjacent interior angles.
   
   Let the interior angle adjacent to the 153° exterior angle be \( y^\circ \). Therefore:
   \[
   y + 153^\circ = 180^\circ
   \]
   Solving for \( y \):
   \[
   y = 180^\circ - 153^\circ = 27^\circ
   \]

3. Now, the sum of the interior angles of a triangle is always 180°. So, the angles in the triangle are:
   - \( x^\circ \) (the angle we need to find),
   - \( 27^\circ \) (the angle we just found), and
   - \( 90^\circ \) (the right angle).

   Using the angle sum property:
   \[
   x + 27^\circ + 90^\circ = 180^\circ
   \]
   Simplifying:
   \[
   x + 117^\circ = 180^\circ
   \]
   \[
   x = 180^\circ - 117^\circ = 63^\circ
   \]

Thus, the value of \( x \) is **63°**.

Would you like more details or have any questions? Here are five related questions you could explore:

1. What is the exterior angle theorem, and how is it used in different types of triangles?
2. How do you calculate the exterior angles for polygons with more sides than a triangle?
3. Can you explain the angle sum property in non-Euclidean geometry?
4. What is the significance of right triangles in trigonometry?
5. How are exterior and interior angles related in quadrilaterals?

**Tip:** Always remember that the sum of the interior angles of a triangle is 180°, regardless of the type of triangle!

A side of the triangle has been extended to form an exterior angle of 153°. Find the value of x°.

Learn how to find the interior angle of a triangle when given an exterior angle of 153°. Use the exterior angle theorem and the sum of interior angles to calculate the value of x in this geometry problem. Suitable for students in Grades 7-9.

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