Question

explore the properties of inscribed angles by following these steps.
what is the measure of ∠abc?
25°

1. make a conjecture. which measures will change if you move vertex b of the inscribed angle? neither
2. move vertex b and observe what happens to the angle measures. was your conjecture correct?

dropdown with yes and no options
circle with points a, b, c; m∠abc = 52°, m⌢ac = 104°

Explanation:

The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. Here, \( m\angle ABC = 52^\circ \) and \( m\widehat{AC}=104^\circ \), so \( \angle ABC=\frac{1}{2}m\widehat{AC} \). When moving vertex \( B \) (while keeping \( A \) and \( C \) fixed), the intercepted arc \( \widehat{AC} \) doesn't change, so the inscribed angle \( \angle ABC \) should remain half of \( \widehat{AC} \). Thus, the conjecture that neither measure changes is correct, so the answer to "Was your conjecture correct?" is "yes".

Answer:

yes