Question

adding and subtracting angles
add or subtract each of these exercises as indicated.

1. $\

$$\begin{array}{r}34^{\\circ} \\\\ +97^{\\circ} \\\\ \\hline\\end{array}$$

$

1. $5^{\circ} 43^{\prime} 18^{\prime \prime}+13^{\circ} 40^{\prime} 26^{\prime \prime}$
2. $\

$$\begin{array}{r}68^{\\circ} 26^{\\prime} \\\\ -54^{\\circ} 17^{\\prime} \\\\ \\hline\\end{array}$$

$

1. $55^{\circ} 9^{\prime} 18^{\prime \prime}-51^{\circ} 57^{\prime} 30^{\prime \prime}$

Explanation:

Step1: Add degrees

For problem 1: \(34^{\circ}+97^{\circ}=(34 + 97)^{\circ}\)

Step2: Calculate the sum

\(34+97 = 131\), so \(34^{\circ}+97^{\circ}=131^{\circ}\)

For problem 5:

Step1: Add degrees, minutes and seconds separately

Degrees: \(5^{\circ}+13^{\circ}=(5 + 13)^{\circ}=18^{\circ}\)
Minutes: \(43'+40'=(43 + 40)'=83'\)
Seconds: \(18''+26''=(18 + 26)''=44''\)

Step2: Convert minutes (since \(60' = 1^{\circ}\))

\(83'=1^{\circ}23'\)

Step3: Add the converted degree to the degree sum

\(18^{\circ}+1^{\circ}23'=19^{\circ}23'\)
So \(5^{\circ}43'18''+13^{\circ}40'26''=19^{\circ}23'44''\)

For problem 9:

Step1: Subtract degrees and minutes separately

Degrees: \(68^{\circ}-54^{\circ}=(68 - 54)^{\circ}=14^{\circ}\)
Minutes: \(26'-17'=(26 - 17)'=9'\)
So \(68^{\circ}26'-54^{\circ}17'=14^{\circ}9'\)

For problem 13:

Step1: Borrow \(1^{\circ}=60'\) and \(1' = 60''\)

\(55^{\circ}9'18''=54^{\circ}69'18''\) (borrow \(1^{\circ}\) for minutes)
\(54^{\circ}69'18''=54^{\circ}68'78''\) (borrow \(1'\) for seconds)

Step2: Subtract degrees, minutes and seconds

Degrees: \(54^{\circ}-51^{\circ}=(54 - 51)^{\circ}=3^{\circ}\)
Minutes: \(68'-57'=(68 - 57)'=11'\)
Seconds: \(78''-30''=(78 - 30)''=48''\)
So \(55^{\circ}9'18''-51^{\circ}57'30''=3^{\circ}11'48''\)

Answer:

1. \(131^{\circ}\)
2. \(19^{\circ}23'44''\)
3. \(14^{\circ}9'\)
4. \(3^{\circ}11'48''\)