Thread: Complementary Angles?

,.,good day,.,
,.somethings been buggling my mind lately,.,.i have encountered this theorem on geometry,.,it says "If two angles are complementary, then both are acute"
so i have this question "is zero degree the complement of 90 degrees???if so,.then both are not acute since acute angles are angles less than 90,.,please help me with this,.,.thnx

Originally Posted by aldrincabrera

theorem on geometry,.,it says "If two angles are complementary, then both are acute" so i have this question "is zero degree the complement of 90 degrees???if

In a course in axiomatic geometry, most authors use this definition:
An angle is the union of two non-collinear rays with a common endpoint.
So that rules out both a degenerate angle and a so-called ‘straight angle’.
In fact, Jay Greenberg has the following theorem in his text:


So strictly speaking we would not have an angle of measure zero.

,.,sir,.,i was proving the theorem and i ended up with this,.plss tell me if im doing it correctly,.
here is my proof.,
let alpha and beta be complementary angles,
then alpha + beta = 90.
we show that alpha < 90 and beta<90.
Suppose alpha >equal to 90 or beta >equal to 90,
then alpha+beta >equal to 90 in either cases.
thus alpha<90 and beta <90,.

am i wrong sir??thnx

Originally Posted by aldrincabrera

,.,sir,.,i was proving the theorem and i ended up with this,.plss tell me if im doing it correctly,.
here is my proof.,
let alpha and beta be complementary angles,
then alpha + beta = 90.
we show that alpha < 90 and beta<90.
Suppose alpha >equal to 90 or beta >equal to 90,
then alpha+beta >equal to 90 in either cases.
thus alpha<90 and beta <90,.

If the sum of two positive numbers is 90 then each must be less than 90.

,.but sir,.,am i on the right track??

Let and be complementary angles so indeed:

If you want to show: and .
You have to do that for positive numbers!

Because if you take and
Then but is not .

So you have to assure you work with positive numbers.