Answer:
To find the value of x in the given diagram where OO is circumscribed about quadrilateral ABCD with an angle measure of 5x°, we can use the properties of the angles in a circle:
1. In a quadrilateral inscribed in a circle, the sum of the opposite angles is equal to 150°.
Given that the angle measure of ABCD is 5x°, we can determine the values of the opposite angles:
2. Angle ABC + Angle CDA = 150°
5x + 5x = 150
10x = 150
x = 15
Therefore, the value of x is 15.
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