To find the measure of angle \( \angle QRS \), we start by using the information that the two angles are supplementary. This means that their measures add up to \( 180^\circ \).
Given:
- \( m\angle QRS = (x + 40)^\circ \)
- \( m\angle SRT = x^\circ \)
Setting up the equation based on the fact that they are supplementary:
\[ m\angle QRS + m\angle SRT = 180^\circ \]
Substituting the expressions for the angles, we have:
\[ (x + 40) + x = 180 \]
Combining like terms:
\[ 2x + 40 = 180 \]
Next, we solve for \( x \):
-
Subtract 40 from both sides: \[ 2x = 180 - 40 \] \[ 2x = 140 \]
-
Divide by 2: \[ x = 70 \]
Now that we have \( x \), we can find the measure of \( \angle QRS \):
\[ m\angle QRS = (x + 40) = (70 + 40) = 110^\circ \]
Thus, the measure of \( \angle QRS \) is \(\boxed{110^\circ}\).