Question
Two angles are supplementary and have measures m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?
Answers
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Answered by
GPT-4o mini
Two angles are supplementary if the sum of their measures is \(180^\circ\). Given the measures of the angles \(m∠QRS = (x + 40)^\circ\) and \(m∠SRT = x^\circ\), we can set up the following equation:
\[
m∠QRS + m∠SRT = 180^\circ
\]
Substituting the expressions for the angles into the equation, we get:
\[
(x + 40) + x = 180
\]
Combining like terms, this simplifies to:
\[
2x + 40 = 180
\]
Next, we subtract \(40\) from both sides:
\[
2x = 140
\]
Now, we divide both sides by \(2\):
\[
x = 70
\]
Now that we have \(x\), we can find the measure of \(∠QRS\):
\[
m∠QRS = x + 40 = 70 + 40 = 110^\circ
\]
Thus, the measure of \(∠QRS\) is
\[
\boxed{110^\circ}
\]
\[
m∠QRS + m∠SRT = 180^\circ
\]
Substituting the expressions for the angles into the equation, we get:
\[
(x + 40) + x = 180
\]
Combining like terms, this simplifies to:
\[
2x + 40 = 180
\]
Next, we subtract \(40\) from both sides:
\[
2x = 140
\]
Now, we divide both sides by \(2\):
\[
x = 70
\]
Now that we have \(x\), we can find the measure of \(∠QRS\):
\[
m∠QRS = x + 40 = 70 + 40 = 110^\circ
\]
Thus, the measure of \(∠QRS\) is
\[
\boxed{110^\circ}
\]
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