Question - Determining the Relationship Between Algebraic Expressions in a Geometric Diagram

The given image shows a geometric diagram with angles labeled in terms of "x". To solve for "x", we can use the fact that the sum of angles in a triangle is 180 degrees.

In triangle QRP:

QR + RP + PQ = 180

Substituting the given expressions, we get:

3x + 4x + 5x = 180

Combine like terms:

12x = 180

Divide both sides by 12 to solve for x:

x = \frac{180}{12}

x = 15