Sure! Let's solve these angle addition problems step by step.
### First Set of Angles
Given:
1. \(36^\circ 24' 23''\)
2. \(45^\circ 52' 36''\)
#### Step 1: Adding the Seconds
First, add the seconds:
[tex]\[23'' + 36'' = 59''\][/tex]
Since the total seconds are less than 60, there's no need to convert to minutes.
#### Step 2: Adding the Minutes
Now, add the minutes:
[tex]\[24' + 52' = 76'\][/tex]
Since \(76'\) exceeds \(60'\), we need to convert the excess into degrees:
[tex]\[76' = 1^\circ 16'\][/tex]
Thus, carry over \(1^\circ\) to the degrees, leaving \(16'\).
#### Step 3: Adding the Degrees
Finally, add the degrees:
[tex]\[36^\circ + 45^\circ + 1^\circ = 82^\circ\][/tex]
Putting it all together:
[tex]\[36^\circ 24' 23'' + 45^\circ 52' 36'' = 82^\circ 16' 59''\][/tex]
### Second Set of Angles
Given:
1. \(36^\circ 45' 23''\)
2. \(53^\circ 32' 18''\)
#### Step 1: Adding the Seconds
First, add the seconds:
[tex]\[23'' + 18'' = 41''\][/tex]
Since the total seconds are less than 60, there's no need to convert to minutes.
#### Step 2: Adding the Minutes
Now, add the minutes:
[tex]\[45' + 32' = 77'\][/tex]
Since \(77'\) exceeds \(60'\), we need to convert the excess into degrees:
[tex]\[77' = 1^\circ 17'\][/tex]
Thus, carry over \(1^\circ\) to the degrees, leaving \(17'\).
#### Step 3: Adding the Degrees
Finally, add the degrees:
[tex]\[36^\circ + 53^\circ + 1^\circ = 90^\circ\][/tex]
Putting it all together:
[tex]\[36^\circ 45' 23'' + 53^\circ 32' 18'' = 90^\circ 17' 41''\][/tex]
### Final Answer
So the results for the given angle addition problems are:
1. [tex]\[36^\circ 24' 23'' + 45^\circ 52' 36'' = 82^\circ 16' 59''\][/tex]
2. [tex]\[36^\circ 45' 23'' + 53^\circ 32' 18'' = 90^\circ 17' 41''\][/tex]
That concludes our calculation.
