Two angles are supplementary and have measures m<QRS = ( x + 40 ) and m<SRT = x What is the measures of <QRS?

Question

180

70

25

110

Answer 1

Two angles are supplementary if their measures add up to 180 degrees. Given the measures of the angles:

• m<QRS = x + 40
• m<SRT = x

We can set up the equation:

\[ m<QRS + m<SRT = 180 \]

Substituting the expressions for the angles:

\[ (x + 40) + x = 180 \]

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:

\[ m<QRS = x + 40 = 70 + 40 = 110 \]

Therefore, the measure of <QRS is:

\[ \boxed{110} \]