https://file.aiquickdraw.com/mathbot/file/17261580653610funuzaf.jpg

The image shows a right-angled triangle with two known angles: one marked \(36^\circ\) and another represented as \((7x - 2)^\circ\). Since it is a right-angled triangle, one of the angles is \(90^\circ\).

### To solve for \(x\):

In a triangle, the sum of the interior angles is always \(180^\circ\). Therefore, we can set up the following equation:

\[
90^\circ + 36^\circ + (7x - 2)^\circ = 180^\circ
\]

Simplifying this equation:

\[
126^\circ + (7x - 2)^\circ = 180^\circ
\]

\[
7x - 2 = 54^\circ
\]

\[
7x = 56^\circ
\]

\[
x = 8
\]

Thus, \(x = 8\).

### To find the unknown angle:

Substituting \(x = 8\) back into the expression for the angle:

\[
7x - 2 = 7(8) - 2 = 56 - 2 = 54^\circ
\]

So, the unknown angle is \(54^\circ\).

Would you like more details, or do you have any further questions?

Here are 5 related questions you can explore:
1. How do we calculate the sum of interior angles in any polygon?
2. How would this problem change if the angle were expressed differently, say \( (5x - 10)^\circ \)?
3. What is the relationship between angles in a right triangle, specifically in terms of trigonometry?
4. How would you apply the Pythagorean theorem to this triangle if side lengths were given?
5. How can we calculate the other sides of the triangle if one side length is known?

**Tip:** When solving for angles in any polygon, always remember that the sum of the interior angles of a triangle is \(180^\circ\).

Solve for x in the triangle with angles 36 degrees, 90 degrees, and (7x - 2) degrees.

Learn how to solve for x in a right-angled triangle with angles 36 degrees, 90 degrees, and an unknown angle represented by (7x - 2) degrees. This problem covers key algebraic concepts and geometry principles. Suitable for students in Grades 7-9.

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