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The image shows a triangle with a right angle and an exterior angle of 154°. You are asked to find the value of \( x \), the unknown interior angle of the triangle. Let's solve for \( x \).

### Step-by-step solution:

1. The sum of the angles on a straight line is always 180°. Therefore, the angle adjacent to the 154° exterior angle is:
   \[
   \text{Adjacent angle} = 180^\circ - 154^\circ = 26^\circ
   \]

2. In a triangle, the sum of all interior angles is 180°. This triangle has a right angle (90°), so the sum of the remaining two angles (including \( x \)) is:
   \[
   90^\circ = x + 26^\circ
   \]

3. Solving for \( x \):
   \[
   x = 90^\circ - 26^\circ = 64^\circ
   \]

Thus, \( x = 64^\circ \).

Would you like more details on the solution, or have any questions? Here are some related questions:

1. What is the sum of the interior angles of a triangle?
2. How are exterior angles related to interior angles in a triangle?
3. Can a triangle have more than one right angle?
4. How do you calculate the remaining angles if two are known in a right triangle?
5. How does the exterior angle theorem apply to this problem?

**Tip:** The exterior angle of a triangle is always equal to the sum of the two non-adjacent interior angles.

Find the value of x in a triangle with a right angle and an exterior angle of 154°.

Solve for the interior angle x in a triangle with a right angle and a 154° exterior angle using the exterior angle theorem and sum of angles on a straight line. Learn the step-by-step approach, suitable for students in Grades 7-9.

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