Question

modeling real life an amusement park ride swings back and forth along a circular arc as shown, where ( mangle eab = 145^circ ) and ( mangle dac = 80^circ ). find ( moverarc{bc} ). round your answer to the nearest tenth.
( moverarc{bc} = square^circ )
explain your reasoning.

Explanation:

Step1: Find the measure of \(\angle BAC\)

Since \(\angle EAB = 145^{\circ}\) and \(\angle EAD\) is a straight angle (\(180^{\circ}\)), then \(\angle DAB=180^{\circ}-\angle EAB = 180 - 145=35^{\circ}\)

Step2: Calculate \(m\overset{\frown}{BC}\)

We know that \(\angle DAC = 80^{\circ}\), and \(\angle BAC=\angle DAC-\angle DAB\)
Substitute the values: \(\angle BAC = 80^{\circ}- 35^{\circ}=45^{\circ}\)
In a circle, the measure of an arc is equal to the measure of its central angle. So \(m\overset{\frown}{BC}=\angle BAC\)

Answer:

\(45.0\)