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 $90^\circ$.