To find the missing angle measures, we can use the information given regarding the angles in triangle ABCD.
Given:
- \( m∠B = 93° \)
- \( m∠BC = 58° \) (presumably this is an angle made with segment BC)
- \( m∠CD = 106° \)
We start by calculating the angles in triangle ABCD:
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We know that the sum of the angles in a triangle is \( 180° \). If we assume that angles A, B, and C are part of the same triangle, we can write:
\[ m∠A + m∠B + m∠C = 180° \]
Substituting the values we have:
\[ m∠A + 93° + 58° = 180° \]
This simplifies to:
\[ m∠A + 151° = 180° \]
Now we can solve for \( m∠A \):
\[ m∠A = 180° - 151° = 29° \]
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Next, to find m∠C, we can use the information regarding m∠CD. In a straight line configuration involving points C and D, if angles C and CD are angles on a straight line, then:
\[ m∠C + m∠CD = 180° \]
Substituting for m∠CD:
\[ m∠C + 106° = 180° \]
Simplifying gives:
\[ m∠C = 180° - 106° = 74° \]
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Finally, angle D can be calculated as follows. If angles A, C, and D form another triangle, we have:
\[ m∠A + m∠C + m∠D = 180° \]
Substituting the known values:
\[ 29° + 74° + m∠D = 180° \]
This gives:
\[ m∠D = 180° - 103° = 77° \]
Putting it all together:
- \( m∠A = 29° \)
- \( m∠C = 74° \)
- \( m∠D = 77° \)
So the final answers are:
- \( m∠A = 29° \)
- \( m∠C = 74° \)
- \( m∠D = 77° \)