To find the measures of angles ∠1 and ∠2, we begin by understanding that their measures are given as follows:
- \( m∠1 = 2x \)
- \( m∠2 = 2x + 7 \)
According to the problem, the sum of these two angles is equal to 135°:
\[ m∠1 + m∠2 = 135° \]
Substituting the expressions for each angle, we have:
\[ 2x + (2x + 7) = 135° \]
Combining like terms:
\[ 4x + 7 = 135° \]
Next, we isolate the term containing \(x\) by subtracting 7 from both sides:
\[ 4x = 135° - 7 \]
\[ 4x = 128° \]
Now, we can solve for \(x\) by dividing both sides by 4:
\[ x = \frac{128°}{4} \]
\[ x = 32° \]
Now we can find the measures of angles ∠1 and ∠2.
Substituting \(x\) back into the expressions for the angles:
\[ m∠1 = 2x = 2(32°) = 64° \]
\[ m∠2 = 2x + 7 = 2(32°) + 7 = 64° + 7° = 71° \]
Thus, the measures of the two angles are:
\[ m∠1 = 64° \quad \text{and} \quad m∠2 = 71° \]