<PRE><B>Question 825029</B>
If the ratio of the measures of the complementary angle to that of the supplementary angle of the given angle is 1:10.
 find the ratio of the given angle with its complementary angle?
:
Let a = the angle
then
{{{(90-a)/(180-a)}}} = {{{1/10}}}
Cross multiply
180- a = 10(90-a)
180 - a = 900 - 10a
-a + 10a = 900 - 180
9a = 720
a = 720/9
a = 80 degrees is the angle
:
&quot; find the ratio of the given angle with its complementary angle?&quot;
{{{80/(90-80)}}} =  {{{80/10}}} = 8:1
</PRE>