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

80°
80 degrees

100°
100 degrees

50°
50 degrees

180°

Answer 1

To find the measure of angle \( m∠QRS \) given that the two angles are supplementary, we can set up the equation based on the information provided:

1. The measure of angle \( m∠QRS = (x + 30)^\circ\)
2. The measure of angle \( m∠SRT = (2x)^\circ\)

Since the angles are supplementary, their sum is \( 180^\circ \):

\[
m∠QRS + m∠SRT = 180^\circ
\]

Substituting the expressions for the angles:

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

Combine like terms:

\[
3x + 30 = 180
\]

To solve for \( x \), subtract 30 from both sides:

\[
3x = 150
\]

Now, divide by 3:

\[
x = 50
\]

Now, we can find \( m∠QRS \):

\[
m∠QRS = x + 30 = 50 + 30 = 80
\]

Thus, the value of \( m∠QRS \) is \( 80^\circ \).

**Final Answer: 80°**