the measure of angle 5 is 3 times the measure of angle 6 and 20 degrees more. Solve the measure of angles 5. Solve the measure of angle 6

Question

the measure of angle 5 is 3 times the measure of angle 6 and 20 degrees more. Solve the measure of angles 5. Solve the measure of angle 6

Answer 1

Let's label angle 5 as a5, and angle 6 as a6.

 

There are two equations that can come from the first sentence.  The first part (the measure of angle 5 is 3 times the measure of angle 6) is:

 

a5 = 3*a6

 

The second part (and 20 degrees more) can be rewritten as "angle 5 is 20 degrees more than angle 6".  This can be written as:

 

a5 = a6 + 20

 

Both need to be solved for, so the second can be inserted into the first:

 

a6 + 20 = 3*a6

 

Subtract a6 from both sides:

 

20 = 2*a6

 

Divide both sides by 2:

 

a6 = 10

 

Insert this into either equation (we'll do the first):

 

a5 = 3*10

 

Simplify:

 

a5 = 30

 

The answers are:  angle 5 is 30 and angle 6 is 10.

 

Please let me know if this helps or if you have more questions!

 

Thank you,

Christopher Himmel