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Se explanation
Step-by-step explanation:
The diagram shows the circle with center Q. In this circle, angle XAY is inscribed angle subtended on the arc XY. Angle XQY is the central angle subtended on the same arc XY.
The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle. Therefore,
The measure of the intercepted arc XY is the measure of the central angle XQY and is equal to 144°.
All angles that have the same endpoints X and Y and vertex lying in the middle of the quadrilateral XAYQ have measures satisfying the condition
because angle XAY is the smallest possible angle subtended on the arc XY in the circle and angle XQY is the largest possible angle in the circle subtended on the arc XY.