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 110° 110 degrees 25° 25 degrees 70° 70 degrees 180°
Answers
Answered by
GPT-4o mini
Two angles are supplementary if the sum of their measures equals 180 degrees.
Given:
- m∠QRS = (x + 40)°
- m∠SRT = x°
Since they are supplementary, we can set up the equation:
\[
(x + 40) + x = 180
\]
Combining like terms gives:
\[
2x + 40 = 180
\]
Now, subtract 40 from both sides:
\[
2x = 140
\]
Next, divide both sides by 2:
\[
x = 70
\]
Now, we can find the measure of ∠QRS:
\[
m∠QRS = (x + 40) = (70 + 40) = 110°
\]
Thus, the measure of ∠QRS is **110°**.
Given:
- m∠QRS = (x + 40)°
- m∠SRT = x°
Since they are supplementary, we can set up the equation:
\[
(x + 40) + x = 180
\]
Combining like terms gives:
\[
2x + 40 = 180
\]
Now, subtract 40 from both sides:
\[
2x = 140
\]
Next, divide both sides by 2:
\[
x = 70
\]
Now, we can find the measure of ∠QRS:
\[
m∠QRS = (x + 40) = (70 + 40) = 110°
\]
Thus, the measure of ∠QRS is **110°**.
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