https://file.aiquickdraw.com/mathbot/file/1727801165526sogktrgo.jpg

The image shows a right triangle with two angles labeled \( x^\circ \) and a \( 90^\circ \) angle. The problem asks which equation can be used to determine the value of \( x \).

### Key Idea:
In any triangle, the sum of the interior angles is always \( 180^\circ \). Since this is a right triangle, one angle is \( 90^\circ \), so the other two angles must sum to \( 90^\circ \).

Let’s break it down:

1. We know that the sum of the two \( x^\circ \) angles and the \( 90^\circ \) angle must equal \( 180^\circ \). This gives:
   \[
   x + x + 90 = 180
   \]
   Simplifying this:
   \[
   2x + 90 = 180
   \]
   Subtract 90 from both sides:
   \[
   2x = 90
   \]
   Divide by 2:
   \[
   x = 45
   \]

### Conclusion:
The correct equation is \( 2x + 90 = 180 \), which corresponds to option **B**.

Do you need further details or have any questions?

### Related Questions:
1. How do we derive the angle sum property of triangles?
2. What is the importance of recognizing a right triangle?
3. How does this principle apply to non-right triangles?
4. Can this method be extended to solve for unknown angles in quadrilaterals?
5. How would the problem change if the triangle were an equilateral triangle?

### Tip:
Always remember the sum of interior angles in a triangle is \( 180^\circ \), and in a right triangle, the two remaining angles must sum to \( 90^\circ \).

The measures of the angles in a triangle are shown here. Which of the following statements is true? A. The equation x + 90 = 180 can be used to determine the value of x. B. The equation 2x + 90 = 180 can be used to determine the value of x. C. The equation 2x + 45 = 180 can be used to determine the value of x. D. The equation x + 90 = 180 can be used to determine the value of x.

Learn how to calculate the angles in a right triangle where two angles are equal, and one angle is 90 degrees. This problem covers key geometric concepts including the sum of angles in a triangle. Suitable for students in Grades 6-8.

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