The sum of the measures of the three angles in any triangle is 180 degrees. The measure of the smallest angle of a certain triangle is half the measure of the s

Question

The sum of the measures of the three angles in any triangle is 180 degrees. The measure of the smallest angle of a certain triangle is half the measure of the second angle. The measure of the largest angle is 68degrees more than 4 times the measure of the smallest. Find the measure of each angle.

Answer 1

Let the angles be a[smallest], b, and c.

 

    a     +     b      +              c    =     180

   b/2   +     b      +    (2b + 68)  = 180

 

 

    b    +     2b      +   4b      +  136     =    360

        7b + 136 =  360

         7b = 224

            b = 32

 

             a = 16

 

             c = 132

 

Check:

       Is      32 + 16 + 132 = 180   ?

                    180 = 180   ?  yes

       Is   16 = 32/2   ?

             16 = 16   ?yes

       Is     4*16 + 68 = 132   ?

                 132 = 132    ?yes

                   

Answer 2

Let x = the measure of the second angle

Let (1/2)x = the measure of the smallest angle

Let 4(1/2)x+ 68 = the measure of the largest angle

 

x + (1/2)x + 4(1/2)x + 68 = 180

(3 1/2)x = 112

(7/2)x = 112

x = 32º

(1/2)x = 16º

2x + 68 = 132º