Question

explore the properties of inscribed angles by following these steps.

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? mac = × m∠abc

m∠abc = 52°
mac = 104°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Step2: Analyze given values

Given \(m\angle ABC = 52^{\circ}\) and \(m\widehat{AC}=104^{\circ}\), and we know the formula \(m\widehat{AC}=k\times m\angle ABC\).

Step3: Calculate the value of \(k\)

Substitute the values into the formula \(104 = k\times52\), then \(k=\frac{104}{52}=2\).

Answer:

2