Mathematics

How many degrees are there in an angle which is one-fifth of its complement?


SOLUTION
In the given figure,
Given angle is 10501050
x+1050=1800x+1050=1800
x=18001050=750x=1800−1050=750
But x+y=1800x+y=1800              (Sum of co-interior angles)
750+y=1800⇒750+y=1800           (Sum of co-interior angles)
y=1800750=1050⇒y=1800−750=1050
Similarly, y+z=1800y+z=1800   (Sum of co-interior angles)
1050+z=1800⇒1050+z=1800
z=18001050=750⇒z=1800−1050=750
Hence, x=750,y=1050,z=750
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