In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of opposite angles equals 180 degrees.
We are given:
- \( m∠A = 78° \)
- \( m∠B = 125° \)
To find \( m∠C \) and \( m∠D \):
- Using the property of opposite angles in cyclic quadrilaterals, we know:
- \( m∠A + m∠C = 180° \)
- \( m∠B + m∠D = 180° \)
Now we can calculate \( m∠C \):
- \( m∠C = 180° - m∠A = 180° - 78° = 102° \)
Next, we can calculate \( m∠D \):
- \( m∠D = 180° - m∠B = 180° - 125° = 55° \)
Thus, we find:
- \( m∠C = 102° \)
- \( m∠D = 55° \)
Therefore, the correct answer is: m∠C = 102°, m∠D = 55°.