To find the measure of angle \( \angle QRS \), we start with the information that these angles are supplementary. This means that their measures add up to 180 degrees.
Given:
- \( m\angle QRS = (x + 40)^\circ \)
- \( m\angle SRT = x^\circ \)
Setting up the equation for supplementary angles: \[ m\angle QRS + m\angle SRT = 180^\circ \] Substituting the expressions provided: \[ (x + 40) + x = 180 \] Combining like terms: \[ 2x + 40 = 180 \] Subtracting 40 from both sides: \[ 2x = 140 \] Dividing by 2: \[ x = 70 \]
Now we can find the measure of \( \angle QRS \): \[ m\angle QRS = x + 40 = 70 + 40 = 110^\circ \]
Thus, the measure of \( \angle QRS \) is \(\boxed{110^\circ}\).