Dont understand How to do

Question

Find the measure of each acute angle in a right triangle where the measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.

Answer 1

"Find the measure of each acute angle in a right triangle where the measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8."

In any triangle the sum of all interior angles is 180 degrees. Thus, in a right triangle the sum of the two acute angles is 90 degrees, since the right angle is 90 degrees itself.

Let's call the first acute angle "a" and the second acute angle "b".

Therefore we get...

a + b = 90

The problem also states: "one acute angle is 3 times the sum of the measure of the other acute angle and 8"

Therefore we get...

a = 3 ( b + 8 )

Since this equation tells us that 3 ( b + 8 ) is the same as a, we can replace (or substitute) a with it in the first equation, and we get...

3 ( b + 8 ) + b = 90

3b + 24 + b = 90

4b + 24 = 90

4b = 66

b = 16.5

Now plug this value into the second equation, and we get...

a = 3 ( 16.5 + 8 )

a = 3 ( 24.5 )

a = 73.5

Verify by adding up all three angles...

90 + 73.5 + 16.5 = 180

Checks out!