Solve Equations with Supplementary Angles Quick Check

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Question
Two angles are supplementary and have measures m∠QRS=(x+40)°
and m∠SRT=x°
. What is the measure of ∠QRS
?(1 point)
Responses

25°
25 degrees

110°
110 degrees

70°
70 degrees

180°
180 degrees
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1 answer

To find the measure of angle ∠QRS, we first need to know that supplementary angles add up to 180 degrees. Given:

  • m∠QRS = (x + 40)°
  • m∠SRT = x°

We can set up the equation:

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

Now, simplify the equation:

\[ 2x + 40 = 180 \]

Next, subtract 40 from both sides:

\[ 2x = 140 \]

Now, divide both sides by 2:

\[ x = 70 \]

Now we can find m∠QRS:

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

Thus, the measure of ∠QRS is:

\[ \boxed{110°} \]