To find the measures of angles ∠1 and ∠2, we can set up an equation based on the information given. We know that the sum of two adjacent angles (∠1 and ∠2) equals 135°.
Given:
- \( m∠1 = 2x \)
- \( m∠2 = 2x + 7 \)
The equation for the sum of the angles is:
\[ m∠1 + m∠2 = 135° \]
Substituting the expressions for \( m∠1 \) and \( m∠2 \):
\[ 2x + (2x + 7) = 135 \]
Combining like terms:
\[ 4x + 7 = 135 \]
Next, subtract 7 from both sides:
\[ 4x = 128 \]
Now, divide both sides by 4:
\[ x = 32 \]
Now that we have \( x \), we can find the measures of the angles:
\[ m∠1 = 2x = 2(32) = 64° \] \[ m∠2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71° \]
Thus, the measures of the angles are:
\[ m∠1 = 64° \] \[ m∠2 = 71° \]
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