Two angles are supplementary with measures m∠QRS=(x+30)°

Question

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:

\[ \boxed{80°} \]