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

(2x)°+21°=90°

Answer 1

To find the equation to solve for \( x \), we start with the fact that supplementary angles sum to 180 degrees. Given that:

• \( m∠QRS = 33° \)
• \( m∠RST = (2x + 21)° \)

We can set up the equation as follows:

\[ m∠QRS + m∠RST = 180° \]

Substituting the values we have:

\[ 33° + (2x + 21)° = 180° \]

Now, combining the constants:

\[ (2x + 33 + 21)° = 180° \]

This simplifies to:

\[ (2x + 54)° = 180° \]

Therefore, the correct equation to solve for \( x \) is:

\[ (2x)° + 54° = 180° \]

So the correct response is:

(2x)° + 54° = 180°.