To find the measure of angle \( \angle QRS \), we start with the fact that two angles are supplementary, which means their measures add up to \( 180^\circ \).
Given:
- \( m\angle QRS = (x + 40)^\circ \)
- \( m\angle SRT = x^\circ \)
According to the definition of supplementary angles:
\[ m\angle QRS + m\angle SRT = 180^\circ \]
Substituting the expressions for the angles:
\[ (x + 40) + x = 180 \]
Simplifying this equation:
\[ 2x + 40 = 180 \]
Subtract \( 40 \) from both sides:
\[ 2x = 140 \]
Now divide by \( 2 \):
\[ x = 70 \]
Now, substitute \( x \) back into the expression for \( m\angle QRS \):
\[ m\angle QRS = (70 + 40)^\circ = 110^\circ \]
Thus, the measure of \( \angle QRS \) is \( 110^\circ \).
The answer is 110°.
4 answers