To find the measures of the angles \( m∠QRS \) and \( m∠SRT \), we start by using the property that supplementary angles sum to \( 180^\circ \).
Given:
- \( m∠QRS = (x + 30)^\circ \)
- \( m∠SRT = (2x)^\circ \)
Since the two angles are supplementary, we can set up the equation:
\[ (x + 30) + (2x) = 180 \]
Combining like terms:
\[ 3x + 30 = 180 \]
Next, we solve for \( x \) by first subtracting \( 30 \) from both sides:
\[ 3x = 150 \]
Now, divide by \( 3 \):
\[ x = 50 \]
Now to find \( m∠QRS \):
\[ m∠QRS = (x + 30) = (50 + 30) = 80^\circ \]
Thus, the value of \( m∠QRS \) is \( 80^\circ \).
The answer is 80°.