Answer:
106°
Step-by-step explanation:
A quadrilateral inside a circle is a cyclic quadrilateral.
It means that the angles opposite are supplementary (add up to 180).
If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.
Since we know A and C, we can write:
A + C = 180
x^2 + 3x = 180
x^2 +3x - 180 = 0
(x+15)(x-12) = 0
x= -15, or x = 12
Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.
Now finding B:
B = 7x - 10
B = 7(12) - 10
B = 74
We also know that B + D = 180, so:
B + D = 180
74 + D = 180
D = 180 - 74 = 106
