Question

explore the angles and arcs of a circle by following these steps.

1. move point a to point d and move point b to point f.

the central angle bca now intercepts the same arc as the inscribed angle fed.
m∠bca = dropdown × m∠fed
dropdown options: 1/2, 1, 2
check button

right side:
m∠bca = 160°
m⌢ba = 160°
m∠fed = 80°
m⌢fd = 160°

image: circle with center c, points d, a, b, f on circumference, e on circumference. red arc from d to b (passing a, f?); segments: ca, cb, be, de.

Explanation:

Step1: Identify given angle measures

We know that \( m\angle BCA = 160^\circ \) and \( m\angle FED = 80^\circ \).

Step2: Find the multiplier

We need to find a number \( x \) such that \( 160^\circ = x\times80^\circ \). Solving for \( x \), we divide both sides by \( 80^\circ \): \( x=\frac{160^\circ}{80^\circ}=2 \). So \( m\angle BCA = 2\times m\angle FED \).

Answer:

2