To solve for $x$, we apply the triangle sum theorem, which states that the sum of the angles in a triangle is $180^\circ$.

The three angles of triangle $QRS$ are:

1. $x^\circ$,
2. $(x+70)^\circ$,
3. $(x+20)^\circ$.

According to the triangle sum theorem: $x + (x+70) + (x+20) = 180$

Simplify the equation:

$x + x + 70 + x + 20 = 180$ $3x + 90 = 180$

Solve for $x$:

$3x = 180 - 90$ $3x = 90$ $x = 30$

Final Answer:

$x = 30^\circ$

Would you like me to verify or explain further?

Related Questions:

1. What is the triangle sum theorem, and how is it derived?
2. What are the measures of the other angles in this triangle?
3. What happens if the triangle sum theorem is applied incorrectly?
4. How does the triangle sum theorem relate to exterior angles of a triangle?
5. Can the triangle sum theorem be applied to other polygon shapes?

Tip: Always double-check your equations by substituting the solution back into the original problem.