Since angles 1 and 2 together form a right angle, we know that:
\[ m∠1 + m∠2 = 90° \]
Given that \( m∠2 = 47° \), we can find \( m∠1 \):
\[ m∠1 + 47° = 90° \] \[ m∠1 = 90° - 47° = 43° \]
Now, we need to determine what angles 3, 4, and 5 measure.
Since rays are emerging from point A and considering the angles formed around point A must sum up to \( 360° \):
\[ m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° \]
Substituting the values we have:
\[ 43° + 47° + m∠3 + m∠4 + m∠5 = 360° \]
Combining the known angles:
\[ 90° + m∠3 + m∠4 + m∠5 = 360° \]
Now, simplify:
\[ m∠3 + m∠4 + m∠5 = 360° - 90° = 270° \]
At this point, we need to assess the relationships among angles 3, 4, and 5. Since rays form straight angles at point A and following the sequence of angles, we recognize that:
- Angles 3 and 4 are supplementary to angle 1 (i.e., \( m∠3 + m∠1 = 180° \)).
- Therefore, we calculate \( m∠3 \):
\[ m∠3 = 180° - m∠1 = 180° - 43° = 137° \]
Now, substituting \( m∠3 = 137° \) back into the equation we derived earlier:
\[ 137° + m∠4 + m∠5 = 270° \]
Rearranging gives us another equation:
\[ m∠4 + m∠5 = 270° - 137° = 133° \]
Without loss of generality, we can assume angle 5 is equal to angle 4 for symmetry and clarity of the solution (as angles 4 and 5 are generally opposite each other when rays are arranged symmetrically). Thus:
\[ m∠4 + m∠4 = 133° \] \[ 2m∠4 = 133° \] \[ m∠4 = \frac{133°}{2} = 66.5° \]
Hence, the measure of \( m∠4 \) is \( 66.5° \).
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