Answer:
see explanation
Step-by-step explanation:
The opposite angles of the inscribed quadrilateral are supplementary, thus
∠ A + ∠ C = 180°, substitute values
14z - 7 + 8z = 180
22z - 7 = 180 ( add 7 to both sides )
22z = 187 ( divide both sides by 22 )
z = 8.5
Thus
∠ A = 14z - 8 = 14(8.5) - 7 = 119 - 7 = 112°
∠ C = 8z = 8(8.5) = 68°
∠ D = 10z = 10(8.5) = 85°
The sum of the 4 interior angles = 360°, thus
∠ B = 360° - (112 + 68 + 85)° = 360° - 265° = 95°
Thus
∠ A = 112°, ∠ B = 95°, ∠ C = 68°, ∠ D = 85°
