WHICH STATEMENT IS TRUE?
a) a right angle has a complement
b)and obtuse angle has a complement
c)the supplement of a right angle is a right angle
d) every angle has a supplement****
I think the correct answer is b. Because it says HAS a complement. So an obtuse angle would have a 90* inside of it.
To determine which statement is true, let's examine each option:
a) "A right angle has a complement."
To find the complement of an angle, you need to determine the angle that, when added to the given angle, equals 90 degrees (the definition of a right angle). Since a right angle measures exactly 90 degrees, it does not have a complement. Therefore, statement a) is false.
b) "An obtuse angle has a complement."
An obtuse angle measures more than 90 degrees. If an angle were to have a complement, the sum of the angle and its complement would be 90 degrees. However, since an obtuse angle is greater than 90 degrees, it cannot have a complement. Hence, statement b) is false.
c) "The supplement of a right angle is a right angle."
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees (the definition of a straight angle). Since a right angle measures 90 degrees, the supplement of a right angle would be 180 degrees minus 90 degrees, which gives you 90 degrees. Therefore, statement c) is true.
d) "Every angle has a supplement."
This statement is true. Every angle, regardless of its measure, has a supplement. The supplement of an angle is found by subtracting the given angle from 180 degrees. This applies to all angles, including acute angles, right angles, and obtuse angles.
In conclusion, among the given options, the true statement is c) "The supplement of a right angle is a right angle," while option d) "Every angle has a supplement" is also true.