Find the measure of each acute angle in a right angle where the measure of one acute angle is 5 times the measure of the other acute angle

We are given that the measure of one acute angle is 5 times the measure of the other acute angle.

Let us assume the measure of the other acute angle = x degree.

First acute angle is 5 times the other, that is = 5x degrees.

Both angles are making a right angle.

A right angle sum upto 90 degrees.

Therefore,

x+5x = 90.

6x = 90.

Dividing both sides by 6, we get

x = 15.

Therefore, other acute angle = 15° and one angle measure = 5 times of 15 that is 75°