Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe

 The measurements of the angles are:  110° ;  50° ;  20°  .

Explanation:

Note:  There are 3 (three) angles in any triangle (by definition).

By definition, all the angles in any triangle add up to 180° .

The problems asks us to find the measure of EACH angle of the triangle.

We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:

     →  " x + (x + 90) + (x + 30) = 180 "  ;

   in which:  "x" is the measure of one of the angles;
                                (specifically, the smallest angle) in the triangle;
              "(x + 90)" is the measure of another one of the angles in the triangle; 
              "(x + 30)" is the measure of another one of the angles in the triangle; 

By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;

  →   x + (x + 90) + (x + 30) = 180 ; 

         x + x + 90 + x + 30 = 180 ;
        
  →    3x + 120 = 180 ;

     Subtract "120" from each side of the equation ;

           3x + 120 − 120 = 180 − 120 ;

to get:      3x  = 60 ;

   Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the equation ;  and to solve for "x" ;

               3x = 60 ;
            
              3x / 3 = 60 / 3 ;
             
                 x = 20 ;

Now, we have the original equation:

x + (x + 90) + (x + 30) = 180 ; 

in which:  x = 20° {the smallest angle) ; 
                "(x + 90)" = "(20 + 90) = 110° ;
                "(x + 30)" = "(20 + 30)" = 50° ;

 The measurements of the angles are:  110° ;  50° ;  20°  .

To check our work:

20 + 110 + 50 =?  180 ?? ;   → 130 + 50 =?  180 ?? ; → Yes!

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