To find the supplement of an angle, we need to subtract the given angle from [tex]\(180^\circ\)[/tex].
Let's go through each angle step by step:
### (i) Finding the supplement of [tex]\(630^\circ\)[/tex]
To find the supplement of [tex]\(630^\circ\)[/tex]:
[tex]\[ \text{Supplement} = 180^\circ - 630^\circ \][/tex]
[tex]\[ \text{Supplement} = -450^\circ \][/tex]
So, the supplement of [tex]\(630^\circ\)[/tex] is [tex]\(-450^\circ\)[/tex].
### (ii) Finding the supplement of [tex]\(1380^\circ\)[/tex]
To find the supplement of [tex]\(1380^\circ\)[/tex]:
[tex]\[ \text{Supplement} = 180^\circ - 1380^\circ \][/tex]
[tex]\[ \text{Supplement} = -1200^\circ \][/tex]
So, the supplement of [tex]\(1380^\circ\)[/tex] is [tex]\(-1200^\circ\)[/tex].
### (iii) Finding the supplement of [tex]\(\frac{3}{5}\)[/tex] of a right angle
A right angle is [tex]\(90^\circ\)[/tex]. So, [tex]\(\frac{3}{5}\)[/tex] of a right angle is:
[tex]\[ \frac{3}{5} \times 90^\circ = \frac{270^\circ}{5} = 54^\circ \][/tex]
To find the supplement of [tex]\(54^\circ\)[/tex]:
[tex]\[ \text{Supplement} = 180^\circ - 54^\circ \][/tex]
[tex]\[ \text{Supplement} = 126^\circ \][/tex]
So, the supplement of [tex]\(\frac{3}{5}\)[/tex] of a right angle is [tex]\(126^\circ\)[/tex].
### Summary
- The supplement of [tex]\(630^\circ\)[/tex] is [tex]\(-450^\circ\)[/tex].
- The supplement of [tex]\(1380^\circ\)[/tex] is [tex]\(-1200^\circ\)[/tex].
- The supplement of [tex]\(\frac{3}{5}\)[/tex] of a right angle is [tex]\(126^\circ\)[/tex].
