To solve for the missing angle measures \( m\angle A \), \( m\angle C \), and \( m\angle D \), we need to understand the relationships between the angles provided.
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Given \( m\angle B = 93^\circ \) and that \( B \) is adjacent to \( C \) and \( D \), we can assume that angles \( A \), \( B \), \( C \), and \( D \) are part of a quadrilateral.
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The sum of the angles in a quadrilateral is \( 360^\circ \). Therefore, we can use the equation: \[ m\angle A + m\angle B + m\angle C + m\angle D = 360^\circ \]
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We know:
- \( m\angle B = 93^\circ \)
- \( m\angle C = 58^\circ \)
- \( m\angle D = 106^\circ \)
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Plugging in the known values: \[ m\angle A + 93^\circ + 58^\circ + 106^\circ = 360^\circ \]
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First, calculate the sum of the known angles: \[ 93 + 58 + 106 = 257^\circ \]
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Now, substitute this sum back into the equation: \[ m\angle A + 257^\circ = 360^\circ \]
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Now, isolate \( m\angle A \): \[ m\angle A = 360^\circ - 257^\circ = 103^\circ \]
Now we have found \( m\angle A \). The angles provided are for \( C \) and \( D \) in the question:
- \( m\angle A = 103^\circ \)
- \( m\angle C = 58^\circ \) (provided)
- \( m\angle D = 106^\circ \) (provided)
Final Answer:
- \( m\angle A = 103^\circ \)
- \( m\angle C = 58^\circ \)
- \( m\angle D = 106^\circ \)