Question 554041: Two complementary angles have measures in the ratio
2:4. What is the measure of the larger angle? Found 2 solutions by Theo, rapaljer:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! ratio of angle x to angle y is 2/4
this means that x/y = 2/4 which means that 4x = 2y which means that y = 4/2x = 2x.
we have y = 2x
if the angles are complementary, then their sum is 90 degrees.
this means that:
x + y = 90
since y = 2x, this means that:
x + 2x = 90 which means that:
3x = 90 which yields:
x = 30 degrees.
this makes y equal to 60 degrees.
you have:
x = 30
y = 60
y is the larger angle so the answer to the question is:
the larger angle equals 60 degrees.
our ratio becomes:
x/y = 2/4 = 30/60
since 2/4 is equivalent to 1/2 and 30/60 is equivalent to 1/2, all the ratios are the same so the answer is good.
x = 30 degrees
y = 60 degrees
ratio of x/y is 1/2 which is the same as 2/4.
larger angle is 60 degrees.
You can put this solution on YOUR website! Two complementary angles would be like x and 90-x. If they are in the ratio of 2:4, you can also write this as 1:2 or 1/2, so
Since means that ,
means that .
2x=90-x
3x=90
x=30, which obviously is the smaller angle.
The larger angle is 90-x= 60.
If you or anyone needs to contact me, my Email address is rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
