Two angles from a complementary pair (sum is 90) one angle is 3x-10 the other angle is x+8

Question

It's 8 th grade math mostly combined number 

Answer 1

This is really an Algebra Problem with a little Geometry.

 

Angle1 = 3x - 10

Angle2 = x + 8

 

Angle1 + Angle 2 = 90 degrees (definition of complementary angles)

 

Substituting the first two equations into the third:

(3x - 10) + (x + 8) = 90

 

the goal is to move all the x's to one side and constants to the other. I'll move x's to the left.

 

3x - 10 + x + 8 = 90 (then combine the x's and the constants)

4x - 2 = 90               (then add 2 to both sides)

4x = 90 + 2

4x = 92                    (divide both sides by 4 so we get the value of one 'x'

x = 92/4 = 23

 

Now take the value 18 and plug it into the two original formulas:

 

angle1 = 3x - 10 = 3 x 23 - 10 = 69 - 10 = 59 degrees

angle2 = x + 8 = 23 + 8 = 31

 

and- important! check to see if the two answers really add up yo 90. 59+31=90. good.

 

[when i originally did this I made a division mistake. Got to the and, checked the numbers and it failed. Had I not checked the answer I would have never known that I had blown it.]