Question 336561
My explanation:
Complementary angles are angles that add up to 90.
For example, 55 degrees and 35 degrees are complementary, they add up to 90
If you were asked,"What is the complement of 25 degrees?" you would 
say 90 - 25 = 65 degrees and is the complement of 25
;
The sum of the measures of two complementary angles is 90 degrees. (we just said that)
Call the two angles, x & y, they are complementary therefore:
x + y = 90
:
Find the measures of two complementary angles whose measures are in the ratio of 1:4.
Therefore:
{{{x/y}}} = {{{1/4}}}
Cross multiply
y = 4x
:
return to the equation x + y  90
Replace y with 4x,
x + 4x = 90
5x = 90
x = {{{90/5}}}
x = 18 degees
We know y = 4x, therefore
y = (4*18) 
y = 72 degrees
:
These two angle add up to 90 and have the ratio of 1:4
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Did this shed some light on complementary angles??