Two supplementary angles have measures m∠QRS=33° and m∠RST=(2x+21)° . What is the equation to solve for x ?(1 point)

Question

Responses

(2x)°+21°=90°
left parenthesis 2 x right parenthesis degrees plus 21 degrees equals 90 degrees

(2x)°+54°=90°
left parenthesis 2 x right parenthesis degrees plus 54 degrees equals 90 degrees

(2x)°+54°=180°
left parenthesis 2 x right parenthesis degrees plus 54 degrees equals 180 degrees

(2x)°+21°=180°

Answer 1

To solve for \( x \), we need to recognize that supplementary angles add up to \( 180^\circ \). Given that \( m∠QRS = 33^\circ \) and \( m∠RST = (2x + 21)^\circ \), we can set up the equation:

\[ m∠QRS + m∠RST = 180^\circ \]

Substituting the known values:

\[ 33^\circ + (2x + 21)^\circ = 180^\circ \]

Now, simplify this:

\[ 33 + 2x + 21 = 180 \]

Combining like terms:

\[ 2x + 54 = 180 \]

Now, isolate \( 2x \):

\[ 2x = 180 - 54 \] \[ 2x = 126 \]

Thus, the correct equation to set up from the problem statement for solving \( x \) is:

\[ (2x)^\circ + 54^\circ = 180^\circ \]

So the correct response is:

\[ (2x)° + 54° = 180° \]