To find the measures of the angles, we start with the information that two angles are supplementary. This means that the sum of the two angles is 180 degrees. Given:
- \( m∠QRS = (x + 40)° \)
- \( m∠SRT = x° \)
We can set up the equation:
\[ (x + 40) + x = 180 \]
Simplifying this gives:
\[ 2x + 40 = 180 \]
Subtracting 40 from both sides:
\[ 2x = 140 \]
Dividing both sides by 2:
\[ x = 70 \]
Now that we have the value of \( x \), we can find \( m∠QRS \):
\[ m∠QRS = x + 40 = 70 + 40 = 110° \]
Therefore, the measure of \( ∠QRS \) is:
\[ \boxed{110°} \]