To solve this, we need to use the properties of a cyclic quadrilateral (a quadrilateral inscribed in a circle). One important property is that the opposite angles of a cyclic quadrilateral sum up to \( 180^\circ \).
Given the angles:
- \( m\angle AB = 54^\circ \)
- \( m\angle BC = 115^\circ \)
- \( m\angle CD = 86^\circ \)
We can find \( m\angle AD \) by using the relationship regarding the angles.
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Finding \( m\angle AD \): \[ m\angle AB + m\angle CD = 180^\circ \] \[ 54^\circ + m\angle AD = 180^\circ \] Solving for \( m\angle AD \): \[ m\angle AD = 180^\circ - 54^\circ = 126^\circ \]
Therefore, the statement \( m\angle AD = 115^\circ \) is incorrect.
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Finding \( m\angle B \): \[ m\angle BC + m\angle AD = 180^\circ \] Substituting \( m\angle AD = 126^\circ \): \[ 115^\circ + m\angle B = 180^\circ \] Solving for \( m\angle B \): \[ m\angle B = 180^\circ - 115^\circ = 65^\circ \] Thus, the statement \( m\angle B = 95.5^\circ \) is incorrect.
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Finding \( m\angle ADC \): We can also find \( m\angle ADC \): \[ m\angle BC + m\angle AD + m\angle CD = 180^\circ \] Substituting the known values: \[ 115^\circ + 126^\circ + 86^\circ != 180^\circ \] Since a correction must be made considering the cyclic nature of the quadrilateral.
Thus, using known angles does not yield \( m\angle ADC = 84.5^\circ \).
Conclusion: Each of the alternative answers presented does not satisfy the conditions derived from the properties of cyclic quadrilaterals. Please recheck the angles and conditions for validity.
Here’s a quick summary of the evaluations:
- \( m\angle AD \neq 115^\circ \)
- \( m\angle ADC \neq 84.5^\circ \)
- \( m\angle B \neq 95.5^\circ \)
Please clarify any additional requirements or constraints.