Explanation:
you mean it is 6° less, right ?
supplement means together they have 180°.
complement means together they have 90°.
x is our angle.
180 - x is the supplement angle.
90 - x is the complement angle.
180 - x = 90 - x - 6
90 = -6
you see, that is not possible.
the difference between the supplementary angle and the complementary angle is always 90°.
e.g.
x = 30°
supplement = 180-30 = 150°
complement = 90-30 = 60°
the difference is : 150 - 60 = 90°
x = 80°
supplement = 180 - 80 = 100°
complement = 90-80 = 10°
the difference is : 100 - 10 = 90°
and so on.
so, again, there is no angle that satisfies that criteria.
either you made a mistake in the problem description, or your teacher tried to be tricky.
remember, as x has also a complementary angle, it must be smaller than 90°.
so, the supplementary angle of x must be larger than 90°, and therefore larger than the complementary angle.
there is no angle, for which the supplementary angle is smaller than the complementary angle.