m∠A = 92°; m∠B = 100°; m∠C = 88°; m∠D = 80°.
The inscribed quadrilateral conjecture says that opposite angles in an inscribed quadrilateral are supplementary. Thus we know that
A+C = 180
(x+2) + (x-2) = 180
Combining like terms we have:
2x = 180
Divide both sides by 2:
2x/2 = 180/2
x = 90
Thus A = x+2 = 90+2 = 92°,
C = x-2 = 90-2 = 88° and
D = x-10 = 90-10 = 80°.
To find the measure of ∠B, we subtract the sum of the three other angles from 360°:
∠B=360 - (92+88+80) = 360-260 = 100°
