Example.1) Complementary Angles

Suppose you have two complementary angles, A = 40∘ and B = 50∘. To find the sum, you can use the fact that complementary angles add up to 90∘ :-

A + B = 40∘ + 50∘ = 90∘

So, the sum of these complementary angles is 90∘.   (Ans.)

Example.2) Supplementary Angles

Now, consider two supplementary angles, X = 120∘ and Y = 60∘. Supplementary angles add up to 180∘, so the sum is:

X + Y = 120∘ + 60∘ = 180∘

The sum of these supplementary angles is 180∘.     (Ans.)

Let's take two angles P = 30∘ and Q = 45∘. These angles are neither complementary nor supplementary. You can directly add their measures:

P + Q = 30∘ + 45∘ = 75∘

So, the sum of these angles is 75∘.         (Ans.)

In summary:

• For complementary angles, you add to get 90∘.
• For supplementary angles, you add to get 180∘.
• For angles that are neither complementary nor supplementary, you simply add their measures.

Always check the given conditions or relationships between the angles, and use the appropriate sum based on whether they are complementary or supplementary.

Example.4) Add 46∘ 37' and 125∘ 48'

Ans.)   As per the given condition we have to add 46∘ 37' and 125∘ 48' -

46∘   37'

+  125∘   48'

_______________

172∘   25'

(In above calculation in One's column addition of 37' + 48' = 85', but we know that 1∘ = 60', so we should deduct 60' from 85' and add to Ten's column by 1∘ and obtained the result is 46∘ + 125∘ + 1∘ = 172∘)

So, the answer is  172∘ 25'     (Ans.

Example.5)  Add 115∘ 57' and 105∘ 48'

Ans.)  As per the given condition we have to add 115∘ 57' and 105∘ 48' -

115∘   57'

+   105∘   48'

_______________

221∘   45'

(In above calculation in One's column addition of 57' + 48' = 105', but we know that 1∘ = 60', so we should deduct 60' from 105' and add to Ten's column by 1∘ and obtained the result is 115∘ + 105∘ + 1∘ = 221∘)

So, the answer is  221∘ 45'     (Ans.

Example.6)  Add 73∘ 39' and 43∘ 34'

Ans.)  As per the given condition we have to add 73∘ 39' and 43∘ 34' -

73∘   39'

+    43∘   34'

_______________

117∘   13'

(In above calculation in One's column addition of 39' + 34' = 73', but we know that 1∘ = 60', so we should deduct 60' from 73' and add to Ten's column by 1∘ and obtained the result is 73∘ + 43∘ + 1∘ = 117∘)

So, the answer is  117∘ 13'     (Ans.