Two supplementary angles have measures m∠QRS=33°

Question

and m∠RST=(2x+21)°
. What is the equation to solve for x
?(1 point)
Responses

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

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

(2x)°+21°=180°
left parenthesis 2 x right parenthesis degrees plus 21 degrees equals 180 degrees

(2x)°+54°=90°

Answer 1

Two angles are supplementary if the sum of their measures is 180 degrees. Given that \( m\angle QRS = 33° \) and \( m\angle RST = (2x + 21)° \), we can write the equation:

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

Substituting the given values into the equation:

\[ 33° + (2x + 21)° = 180° \]

Now we can combine like terms:

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

This simplifies to:

\[ 54 + 2x = 180 \]

To isolate \( 2x \), we subtract 54 from both sides:

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

Thus, the equation that corresponds to the problem is:

\[ (2x)° + 54° = 180° \]

So the correct response is:

\[ (2x)° + 54° = 180° \]