Inscribed Angle Math Example 4

Solution

1. 1
   Step 1: Use the property that opposite angles of a cyclic quadrilateral are supplementary: $\angle A + \angle C = 180°$.
2. 2
   Step 2: Solve for $\angle C$: $\angle C = 180° - 82° = 98°$.
3. 3
   Step 3: To find $\angle ADC$, note it intercepts arc $ABC$ (the arc from $A$ to $C$ not containing $D$). Arc $ABC = \text{arc } AB + \text{arc } BC = 96° + 110° = 206°$.
4. 4
   Step 4: Apply the Inscribed Angle Theorem: $\angle ADC = \frac{1}{2} \times 206° = 103°$.