Question

explore the properties of inscribed angles by following these steps.
the inscribed angle? neither

1. move vertex b and observe what happens to the angle measures. was your conjecture correct? yes
2. what is the relationship between inscribed angle abc and arc ac? ( mwidehat{ac} = \boldsymbol{\text{dropdown}} \times mangle abc ) (dropdown options: 1/2, 1, 2)

check
circle with points a, b, c; ( mangle abc = 52^circ ), ( mwidehat{ac} = 104^circ )

Explanation:

Step1: Recall the inscribed angle theorem

The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. So, if \( m\angle ABC \) is the inscribed angle and \( m\widehat{AC} \) is the intercepted arc, then \( m\widehat{AC} = 2\times m\angle ABC \).

Step2: Verify with given values

We are given \( m\angle ABC = 52^\circ \) and \( m\widehat{AC} = 104^\circ \). Let's check the relationship: \( 2\times52^\circ = 104^\circ \), which matches \( m\widehat{AC} \). So the multiplier is 2.

Answer:

2