The complement of the supplement of an obtuse angle is always:
A) an acute angle
B) an obtuse angle
C) a straight angle
D) a right angle
Is it D?
So it is a
To determine the complement of the supplement of an obtuse angle, we first need to understand what each term means:
1. Complement: The complement of an angle is the angle that, when added to the given angle, results in 90 degrees (a right angle). So, if we have an angle x, its complement would be 90 - x.
2. Supplement: The supplement of an angle is the angle that, when added to the given angle, results in 180 degrees (a straight angle). So, if we have an angle y, its supplement would be 180 - y.
Now, let's find the complement of the supplement of an obtuse angle:
Since an obtuse angle is greater than 90 degrees (it's between 90 and 180 degrees), let's call it angle z.
The supplement of angle z would be 180 - z.
The complement of the supplement of angle z would be 90 - (180 - z).
By simplifying the expression, we get:
90 - (180 - z) = z - 90
Therefore, the complement of the supplement of an obtuse angle is always: z - 90.
Now, looking at the given options, we can see that option D) a right angle represents 90 degrees. Therefore, the correct answer is indeed D) a right angle.
say 179 degrees
supplement = 1 degree
complement of supplement = 89 degrees
say 91 degrees
supplement = 89 degrees
complement of supplement = 1 degree
so between 0 and 90