Question
Find Missing Angles Quick Check
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Question
There are angles whose measures add to 180°
. Their measures are: m∠A=67°
, m∠B=(2x+20)°
, and m∠C=x°
. What is the measure of ∠B
?(1 point)
Responses
62°
62 degrees
180°
180 degrees
82°
82 degrees
31°
31 degrees
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Answers
GPT-4o mini
To find the measure of \(\angle B\), we need to set up an equation based on the information given about the angles. We know that the sum of the angles is \(180^\circ\):
\[
m∠A + m∠B + m∠C = 180°
\]
Given:
- \(m∠A = 67°\)
- \(m∠B = (2x + 20)°\)
- \(m∠C = x°\)
Substituting in these values, we have:
\[
67° + (2x + 20)° + x° = 180°
\]
Combining like terms:
\[
67° + 20° + 2x + x = 180°
\]
\[
87° + 3x = 180°
\]
Now, isolate \(x\) by subtracting \(87°\) from both sides:
\[
3x = 180° - 87°
\]
\[
3x = 93°
\]
Now, divide by 3:
\[
x = \frac{93°}{3} = 31°
\]
Now that we found \(x\), we can substitute back to find \(m∠B\):
\[
m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82°
\]
Thus, the measure of \(\angle B\) is:
\[
\boxed{82°}
\]
\[
m∠A + m∠B + m∠C = 180°
\]
Given:
- \(m∠A = 67°\)
- \(m∠B = (2x + 20)°\)
- \(m∠C = x°\)
Substituting in these values, we have:
\[
67° + (2x + 20)° + x° = 180°
\]
Combining like terms:
\[
67° + 20° + 2x + x = 180°
\]
\[
87° + 3x = 180°
\]
Now, isolate \(x\) by subtracting \(87°\) from both sides:
\[
3x = 180° - 87°
\]
\[
3x = 93°
\]
Now, divide by 3:
\[
x = \frac{93°}{3} = 31°
\]
Now that we found \(x\), we can substitute back to find \(m∠B\):
\[
m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82°
\]
Thus, the measure of \(\angle B\) is:
\[
\boxed{82°}
\]