Tell me what each angle is in the following triangle: angle 1 is 8x, angle 2 is 2x+3, angle 3: 30 degrees. give me the two answers. *

 117.6° ;  32.4° .

Explanation:

Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.   

We are given the following:

We have a triangle.

Angle 1:  m∡1 = (8x) ;

Angle 2:  m∡2 = (2x + 3) ;

Angle 3:  m∡3 = 30.

We are asked to find:  "m∡1"  and " m∡2" .

Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.

   So, " m∡1 + m∡2 + m∡3 = 180 " . 

Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation;  then solve for "x" ;  then substitute that solved value for "x" into the given expressions for BOTH  "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ; 

 
                m∡1 + m∡2 + m∡3 = 180  ; 

             8x + (2x + 3) + 30 = 180 ;

             8x + 2x + 3 + 30 = 180 ;

  Combine the "like terms" on the 'left-hand side" of the equation; to simplify:

            +8x + 2x = +10x ;

              +3 + 30 = +33 ; 

  Rewrite the entire equation, as:

         10x + 33 = 180 ; 

 Now, subtract "33" from EACH SIDE of the equation:

         10x + 33 − 33 = 180 − 33 ;

 to get:

         10x    =   147 ;  

   Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" : 

         10x / 10 = 147 / 10 ; 

   to get: 

              x = 14.7 ;

    Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m∡1" and "m∡2";  as follows:


Angle 1:  "(8x)" = 8*(14.7) =  117.6° ; 

Angle 2:  "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;

These are the two answers; that is the 2 (TWO) values asked for in the question:   117.6° ;  32.4° .

 Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m∡3 = 30°); all add up to 180° ?

Let us check:

   m∡1  +  m∡2  +  m∡3 = 180 ; 

Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?

   → 117.6 + 32.4 + 30 = ? 180 ??

   → 117.6 + 32.4 = 150  ;   → 150 + 30 =? 180 ?  Yes!