Question

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

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:

\[
\boxed{110}
\]