Question
Solve Equations with Adjacent Angles Practice
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Question
Two adjacent angles form a resulting angle with measure 160°
. m∠1=3x°
and m∠2=(2x+10)°
. Solve for x
. What are the two unknown angles’ measurements?(1 point)
m∠1=
°
, m∠2=
°
Answers
GPT-4o mini
Given the adjacent angles \( m∠1 \) and \( m∠2 \) such that their sum is \( 160^\circ \):
1. \( m∠1 = 3x \)
2. \( m∠2 = 2x + 10 \)
The equation representing the sum of the angles is:
\[
m∠1 + m∠2 = 160^\circ
\]
Substituting the expressions for \( m∠1 \) and \( m∠2 \):
\[
3x + (2x + 10) = 160
\]
Now, combine like terms:
\[
3x + 2x + 10 = 160
\]
\[
5x + 10 = 160
\]
Next, subtract 10 from both sides:
\[
5x = 150
\]
Now, divide both sides by 5:
\[
x = 30
\]
Now that we have \( x \), we can find the measurements of the angles:
1. \( m∠1 \):
\[
m∠1 = 3x = 3(30) = 90^\circ
\]
2. \( m∠2 \):
\[
m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70^\circ
\]
Thus, the measurements are:
- \( m∠1 = 90^\circ \)
- \( m∠2 = 70^\circ \)
1. \( m∠1 = 3x \)
2. \( m∠2 = 2x + 10 \)
The equation representing the sum of the angles is:
\[
m∠1 + m∠2 = 160^\circ
\]
Substituting the expressions for \( m∠1 \) and \( m∠2 \):
\[
3x + (2x + 10) = 160
\]
Now, combine like terms:
\[
3x + 2x + 10 = 160
\]
\[
5x + 10 = 160
\]
Next, subtract 10 from both sides:
\[
5x = 150
\]
Now, divide both sides by 5:
\[
x = 30
\]
Now that we have \( x \), we can find the measurements of the angles:
1. \( m∠1 \):
\[
m∠1 = 3x = 3(30) = 90^\circ
\]
2. \( m∠2 \):
\[
m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70^\circ
\]
Thus, the measurements are:
- \( m∠1 = 90^\circ \)
- \( m∠2 = 70^\circ \)