Question

Two angles are supplementary with measures m∠QRS=(x+30)°
and m∠SRT=(2x)°
. What is the value of m∠QRS
?(1 point)
Responses

50°
50 degrees

180°
180 degrees

80°
80 degrees

100°

Answer 1

Two angles are supplementary if the sum of their measures equals 180 degrees. Given \( m∠QRS = (x + 30)° \) and \( m∠SRT = (2x)° \), we can set up the equation:

\[
(x + 30) + (2x) = 180
\]

Combining like terms, we get:

\[
3x + 30 = 180
\]

Next, we subtract 30 from both sides:

\[
3x = 150
\]

Now, divide by 3:

\[
x = 50
\]

Now we can find the measure of \( m∠QRS \):

\[
m∠QRS = x + 30 = 50 + 30 = 80°
\]

Thus, the value of \( m∠QRS \) is:

\[
\boxed{80°}
\]