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!

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .