Question
Question
Two angles are supplementary with measures m∠QRS=(x+30)°
and m∠SRT=(2x)°
. What is the value of m∠QRS
?(1 point)
Responses
50°
50 degrees
100°
100 degrees
80°
80 degrees
180°
Two angles are supplementary with measures m∠QRS=(x+30)°
and m∠SRT=(2x)°
. What is the value of m∠QRS
?(1 point)
Responses
50°
50 degrees
100°
100 degrees
80°
80 degrees
180°
Answers
GPT-4o mini
To find the measures of the angles \( m∠QRS \) and \( m∠SRT \), we start by using the property that supplementary angles sum to \( 180^\circ \).
Given:
- \( m∠QRS = (x + 30)^\circ \)
- \( m∠SRT = (2x)^\circ \)
Since the two angles are supplementary, we can set up the equation:
\[
(x + 30) + (2x) = 180
\]
Combining like terms:
\[
3x + 30 = 180
\]
Next, we solve for \( x \) by first subtracting \( 30 \) from both sides:
\[
3x = 150
\]
Now, divide by \( 3 \):
\[
x = 50
\]
Now to find \( m∠QRS \):
\[
m∠QRS = (x + 30) = (50 + 30) = 80^\circ
\]
Thus, the value of \( m∠QRS \) is \( 80^\circ \).
The answer is **80°**.
Given:
- \( m∠QRS = (x + 30)^\circ \)
- \( m∠SRT = (2x)^\circ \)
Since the two angles are supplementary, we can set up the equation:
\[
(x + 30) + (2x) = 180
\]
Combining like terms:
\[
3x + 30 = 180
\]
Next, we solve for \( x \) by first subtracting \( 30 \) from both sides:
\[
3x = 150
\]
Now, divide by \( 3 \):
\[
x = 50
\]
Now to find \( m∠QRS \):
\[
m∠QRS = (x + 30) = (50 + 30) = 80^\circ
\]
Thus, the value of \( m∠QRS \) is \( 80^\circ \).
The answer is **80°**.