Answer:
A = 94°
B = 102°
C = 86°
D = 78°
Step-by-step explanation:
Angles inside a quadrilatril add up to 360°.
Opposite angles in a cyclic quadrailtaril (a quadrilateral with every corner touching the circle) add up to 180°.
A + B+ C + D = 360°
A + C = 180°
B + D = 180°
(x + 6) + B + (x - 2) + (x - 10) = 360
(x + 6) + (x - 2) = 180
Simplify:
(x + x) + (6 - 2) = 2x + 4 = 180
Solve to find x:
2x + 4 = 180
2x = 180 - 4
2x = 176
x = 88°
Substitute it in to check it's right.
(x + 6) + (x - 2) = 180
(88 + 6) + (88 - 2) = 180
94 + 86 = 180
Substitute this into the other equation to find B:
(x + 6) + B + (x - 2) + (x - 10) = 360°
(88 + 6) + B + (88 - 2) + (88 - 10) = 360°
94 + B + 86 + 78 = 360°
Rearrange to find B:
B = 360 - 94 - 86 - 78
B = 102°
A = 94°
B = 102°
C = 86°
D = 78°
