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.)