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

100°
100 degrees

50°
50 degrees

180°
180 degrees

80°

Answer 1

To find the measure of angle \( \angle QRS \) and knowing that the two angles \( m\angle QRS \) and \( m\angle SRT \) are supplementary, we can set up the following equation:

\[ m\angle QRS + m\angle SRT = 180° \]

Substituting the expressions for the angles:

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

Now, combine like terms:

\[ 3x + 30 = 180 \]

Next, subtract 30 from both sides:

\[ 3x = 150 \]

Now, divide by 3:

\[ x = 50 \]

Now that we have the value of \( x \), we can find \( m\angle QRS \):

\[ m\angle QRS = x + 30 = 50 + 30 = 80° \]

Thus, the value of \( m\angle QRS \) is:

\[ \boxed{80°} \]