Given that angles 1 and 2 together form a right angle, we can express that as:
\[ m∠1 + m∠2 = 90° \]
Since \( m∠2 = 47° \), we can find \( m∠1 \):
\[ m∠1 = 90° - m∠2 = 90° - 47° = 43° \]
Next, we need to consider how the rays at point A are oriented. Assume angles 3, 4, and 5 follow angles 1 and 2 in a circular sequence (clockwise).
Since angles 1 and 2 are the first two angles, angles 3, 4, and 5 will follow them. Angles 1, 2, 3, 4, and 5 together are arranged in a complete circle, which means:
\[ m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° \]
Using the values we have:
\[ 43° + 47° + m∠3 + m∠4 + m∠5 = 360° \]
This can be simplified to:
\[ 90° + m∠3 + m∠4 + m∠5 = 360° \]
Thus:
\[ m∠3 + m∠4 + m∠5 = 360° - 90° = 270° \]
Now, without loss of generality, we typically assume that angles 3, 4, and 5 are equal since the problem does not provide further information. So, let’s assume:
\[ m∠3 = m∠4 = m∠5 \]
Let \( x = m∠3 = m∠4 = m∠5 \), then we have:
\[ x + x + x = 270° \] \[ 3x = 270° \] \[ x = 90° \]
Therefore, we can find:
\[ m∠4 = 90° \]
In conclusion, the measure of angle 4 is:
\( m∠4 = 90° \)
1 answer