In every triangle, the sum of the interior angles is 180°. The sum of the angles of this triangle is
[tex] 32+(2x-15)+(x-5) = 2x+x+32-15-5 = 3x+12[/tex]
and we want this sum to be 180, so we can write the following equation:
[tex] 3x+12 = 180 [/tex]
subtract 12 from both sides:
[tex] 3x = 168 [/tex]
divide both sides by 3:
[tex] x = \cfrac{168}{3} = 56 [/tex]
Now we can plug this value for x in the expressions for the two unknown angle to get their value:
[tex] B = x-5 = 56-5 = 51,\quad C = 2x-15 = 2\cdot 56-15 = 112-15 = 97 [/tex]
