find the value of each variable. for the circle, the dot represents the center. a = (simplify your answer.)

Explanation:

Step1: Recall circle - quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary (their sum is 180°).

Step2: Set up an equation for the given angles

We know that one pair of opposite angles in the cyclic - quadrilateral are (x) and (130^{\circ}). So, (x + 130^{\circ}=180^{\circ}).

Step3: Solve for (x)

Subtract (130^{\circ}) from both sides of the equation: (x=180^{\circ}-130^{\circ}=50^{\circ}). The other pair of opposite angles are (y) and (90^{\circ}). So, (y + 90^{\circ}=180^{\circ}).

Step4: Solve for (y)

Subtract (90^{\circ}) from both sides of the equation: (y=180^{\circ}-90^{\circ}=90^{\circ}).

Answer:

If the variables are (x) and (y) (assuming the angles are labeled as such), (x = 50), (y = 90)