# CLASS-6SUBTRACTION OF ANGLE

SUBTRACTION OF ANGLE -

Example.1) Subtracting Angles

Suppose you have two angles, A = 80∘ and B = 45∘, and you want to find the difference A − B. Simply subtract the measure of the second angle from the measure of the first angle:

A − B = 80∘ − 45∘ = 35∘

So, A − B is 35∘.         (Ans.)

Example.2) Subtracting Angles in a Triangle

Consider a triangle with angles X = 60∘, Y = 45∘, and Z = 75∘. If you want to find the measure of angle Z, you can use the fact that the sum of angles in a triangle is 180∘. Thus:

Z = 180∘ − (X + Y)

Z = 180∘ − (60∘ + 45∘) = 180∘ − 105∘ = 75∘

So, the measure of angle Z is 75∘.       (Ans.)

Note: Always be aware of the specific context and relationships between the angles when performing subtraction. If the angles are part of a geometric figure (e.g., triangle, quadrilateral), use the properties of that figure to determine the relationship between the angles.

Example.3)  Subtract 53∘ 32' from 75∘  56'

Ans.)  As per the given condition, we have to subtract 53∘ 32' from 75∘  56'.

75∘    56'

-     53∘    32'

_______________

22∘    24'

So, the required answer is 22∘  24'       (Ans.)

Example.4)  Subtract 58∘  56' from 115∘  34'

Ans.) As per the given condition, we have to subtract 58∘  56' from 115∘  34'

115∘   34'

-   58∘   56'

_______________

Here, we can observe that in Ten's column 34' < 56', so to subtract 56' from 34' is not possible. As we know that, 1∘ = 60', so we should add 60' with 34' and now we can deduct 56' from (34' + 60'). Now we should deduct 1∘ from Ten's column (115∘ - 58∘ - 1∘) .

115∘   (34'+ 60')

-    58∘    56'

1∘

___________________

115∘    94'

-    57∘    56'

________________

58∘    38'

So, the required result is  58∘ 38'          (Ans.)

Example.5)  Subtract 73∘  32' from 35∘  57'

Ans.) As per the given condition, we have to subtract 73∘  32' from 35∘  57'

73∘    32'

-    35∘    57'

_______________

Here, we can observe that in Ten's column 32' < 57', so to subtract 57' from 32' is not possible. As we know that, 1∘ = 60', so we should add 60' with 32' and now we can deduct 57' from (32' + 60'). Now we should deduct 1∘ from Ten's column (73∘ - 35∘ - 1∘) .

73∘    (32'+ 60')

-    35∘    57'

1∘

____________________

73∘    92'

-    34∘    57'

________________

39∘    35'

So, the required result is  39∘ 35'          (Ans.)