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

180°
180 degrees

80°
80 degrees

50°
50 degrees

100°

Answer 1

Since the angles are supplementary, their measures add up to 180 degrees.

You have:

• \( m∠QRS = (x + 30)° \)
• \( m∠SRT = (2x)° \)

Setting up the equation:

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

Combining like terms:

\[ 3x + 30 = 180 \]

Subtracting 30 from both sides:

\[ 3x = 150 \]

Dividing by 3:

\[ x = 50 \]

Now substitute \( x \) back into the expression for \( m∠QRS \):

\[ m∠QRS = (50 + 30)° = 80° \]

Thus, the value of \( m∠QRS \) is \( \boxed{80} \) degrees.