two supplementary angles are in the ratio 4:5.What is the measure of the complementary angle of the the shorter angle?
a)10 b)40 c)20 d)25 
PLEASE SEND THE ANSWER ASAP

Dear student,
 

Let the two angles be 4x and 5x.

Since the angles are given as supplementary, therefore their sum must be equal to 

This can also be written as

Dividing both sides of equation by 9, we get

The two angles become

Also,

Hence,and  are the measure of two supplementary angles.

The shorter angle is 80,
And the sum of the complementary angles is 90 degrees.
Hence the angle complementary to the shorter angle = 90-80=10 degrees

Correct answer is A.

Regards