Question

these exercises require division of angles. determine the value of each. (123°43) ÷ 5 36°2444 44°2436 24°3644 24°4436

Explanation:

Step1: Divide degrees

First, divide \(123^{\circ}\) by \(5\): \(\frac{123}{5}=24.6^{\circ}\). The integer part is \(24^{\circ}\), and the decimal part \(0.6^{\circ}\) is converted to minutes. Since \(1^{\circ} = 60'\), then \(0.6\times60 = 36'\).

Step2: Add remaining minutes and divide

We had \(43'\) originally. Now we have \((36 + 43)'\) to divide by \(5\). \(\frac{79}{5}=15.8'\). The integer part is \(15'\), and the decimal part \(0.8'\) is converted to seconds. Since \(1'=60''\), then \(0.8\times60 = 48''\). But wait, let's do it another way.

We know that \(123^{\circ}43'=(123\times60 + 43)'=(7380+43)' = 7423'\). Then \(\frac{7423}{5}=1484.6'\). \(1484\div60 = 24^{\circ}44'\) (because \(1484 = 24\times60+44\)), and \(0.6\times60=36''\)

Answer:

\(24^{\circ}44'36''\)