If two angles are supplementary, their measures add up to 180 degrees.
Given:
- \( m∠QRS = (x + 40)° \)
- \( m∠SRT = x° \)
We can set up the equation:
\[ m∠QRS + m∠SRT = 180° \]
Substituting the expressions for the angles:
\[ (x + 40) + x = 180 \]
Combine like terms:
\[ 2x + 40 = 180 \]
Now, subtract 40 from both sides:
\[ 2x = 180 - 40 \] \[ 2x = 140 \]
Now, divide by 2:
\[ x = 70 \]
Now we can find the measure of \( m∠QRS \):
\[ m∠QRS = x + 40 = 70 + 40 = 110° \]
Therefore, the measure of \( ∠QRS \) is \( \boxed{110°} \).