Given a circle with center O, points A and B on the circle, and point D on the circle such that arc AB has a measure of $80°$, what is the measure of angle BDA, where BDA is an inscribed angle that intercepts arc AB?

• A. $80°$
• B. $20°$
• C. $40°$
• D. $160°$

Answer: (C)

Verified step by step guidance

1. Recall the Inscribed Angle Theorem, which states that an inscribed angle in a circle is half the measure of the arc it intercepts. In other words, if an inscribed angle intercepts an arc of measure \( x \) degrees, then the angle measures \( \frac{x}{2} \) degrees.
2. Identify the given information: the arc \( AB \) measures \( 80^\circ \), and \( \angle BDA \) is an inscribed angle intercepting this arc.
3. Apply the Inscribed Angle Theorem to find \( \angle BDA \). Since \( \angle BDA \) intercepts arc \( AB \), its measure is half of \( 80^\circ \).
4. Write the formula for the angle measure: \( \angle BDA = \frac{1}{2} \times 80^\circ \).
5. Simplify the expression to find the measure of \( \angle BDA \) (do not calculate the final numeric value here, just set up the expression).