Inscribed Angle Math Example 2

Solution

1. 1
   Step 1: Note that $\angle ABC$ and $\angle ADC$ both intercept the same arc $AC$ from the same side of the chord $AC$ (both vertices on the major arc side).
2. 2
   Step 2: By the Inscribed Angle Theorem, any inscribed angle intercepting the same arc has the same measure: $\angle ADC = \frac{1}{2} \times \text{arc } AC$.
3. 3
   Step 3: Substitute: $\angle ADC = \frac{1}{2} \times 134° = 67°$.
4. 4
   Step 4: Conclude that both $\angle ABC$ and $\angle ADC$ equal $67°$, illustrating that inscribed angles intercepting the same arc are congruent.