Two angles are supplementary and have measures m∠QRS=(x+40)°

Question

and m∠SRT=x°
. What is the measure of ∠QRS
?(1 point)
Responses

180°
180 degrees

70°
70 degrees

110°
110 degrees

25°

Answer 1

Two angles are supplementary if the sum of their measures equals 180 degrees.

Given:

• \( m∠QRS = (x + 40)° \)
• \( m∠SRT = x° \)

Setting up the equation for supplementary angles, we have:

\[ (x + 40) + x = 180 \]

Combining like terms:

\[ 2x + 40 = 180 \]

Subtracting 40 from both sides:

\[ 2x = 140 \]

Dividing by 2:

\[ x = 70 \]

Now, we can find the measure of \( m∠QRS \):

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

Thus, the measure of \( ∠QRS \) is:

110 degrees.