Two angles are supplementary with measures m∠QRS=(x+30)° and m∠SRT=(2x)° . What is the value of m∠QRS ?(1 point)

Question

Responses

50°
50 degrees - incorrect

80°
80 degrees - no response given

100°
100 degrees - no response given

180°

Answer 1

To find the measures of the angles, we start with the information given that the angles are supplementary, meaning they add up to 180 degrees.

1. We know:

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

2. Since they are supplementary: \[ (x + 30) + (2x) = 180 \]

3. Combine the terms: \[ 3x + 30 = 180 \]

4. Subtract 30 from both sides: \[ 3x = 150 \]

5. Divide by 3: \[ x = 50 \]

6. Now, substitute \( x = 50 \) back to find \( m∠QRS \): \[ m∠QRS = (50 + 30)° = 80° \]

Therefore, the value of \( m∠QRS \) is 80 degrees.