2x+1is one angle and x-7 is another. when these two angles are complementary angles what is x?

Complementary angles are two angles whose measures add to a sum of 90 degrees. This can be expressed as the following formula:

A1 + A2 = 90

Substitute any known values into the equation above:

(2x + 1) + (x – 7) = 90
2x + 1 + x – 7 = 90

Combine like terms:

3x – 6 = 90

Add 6 to both sides of the equation:

3x = 96

Divide 3 from both sides of the equation:

x = 32

When (2x + 1) and (x – 7) are complementary, “x” is equal to 32.

I hope this helps!

Step-by-step explanation:

Hi, saw your comments, TY :)

this is super tricky b/c they tell us at the top that the triangles are similar so we have to know that we can use that triangle relation to make an equation. It just seem like to me, that you'd not see this  "connection"  where

the smaller triangle is CDE and the bigger one is QPR , so the side can be the lower case of those letters..  the side opposite of the angle is the lower case letter like the angle, soo

p = 2x + 16

r = 33

e = 8

c = 6

then the triangles have that similar triangle relation, of

p = e

r = c

so the fractional relations ship between  e/p  = c /r  you could also make it work by doing  p/e = r/c   but.. you have to keep the bigger triangle and smaller one in the same place for each fraction.  So it's important to keep that clear, which is which

let's use the fractions this way

p/e = r/c  , it seems easiest to me, plug in the values,  

2x + 16 / 8 = 33 / 6  ( now some algebra,  where all mistakes happen :P)

2x + 16 = 8 ( 33 / 6 )   ( times 8 on both sides )

2x + 16 = 4 ( 33 / 3 )         ( I just reduced by 2 )

2x + 16 = 4 ( 11 )  

2x + 16 = 44

2x  = 44 - 16

2x = 28  

x = 14                  ( divide by 2 on both sides )

Yay,  you can check to see if it's right by plugging 14 in for x and seeing if the  p/e = r/c relationship works, I did, and it does :P  but try it just for practice :)