To find the measures of angles \( \angle 1 \) and \( \angle 2 \), we can use the information given about their measures and the resulting angle.
We know that:
- \( m\angle 1 = (2x)^\circ \)
- \( m\angle 2 = (2x + 7)^\circ \)
- The sum of the two angles is \( 135^\circ \).
We can write the equation as:
\[ m\angle 1 + m\angle 2 = 135^\circ \]
Substituting the expressions for \( m\angle 1 \) and \( m\angle 2 \):
\[ 2x + (2x + 7) = 135 \]
Now, combine like terms:
\[ 2x + 2x + 7 = 135 \]
\[ 4x + 7 = 135 \]
Next, we will isolate \( x \) by first subtracting 7 from both sides:
\[ 4x = 135 - 7 \]
\[ 4x = 128 \]
Now, divide both sides by 4:
\[ x = \frac{128}{4} \]
\[ x = 32 \]
Now that we have the value of \( x \), we can find the measures of the angles:
- For \( m\angle 1 \):
\[ m\angle 1 = 2x = 2(32) = 64^\circ \]
- For \( m\angle 2 \):
\[ m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71^\circ \]
Thus, the measures of the angles are:
- \( m\angle 1 = 64^\circ \)
- \( m\angle 2 = 71^\circ \)
Final Answers:
- \( m\angle 1 = 64^\circ \)
- \( m\angle 2 = 71^\circ \)
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