Question

Find the measure of angle ABC

Answer 1

In every triangle, the sum of the interior angles is 180°. The sum of the angles of this triangle is

$32+(2x-15)+(x-5) = 2x+x+32-15-5 = 3x+12$

and we want this sum to be 180, so we can write the following equation:

$3x+12 = 180$

subtract 12 from both sides:

$3x = 168$

divide both sides by 3:

$x = \cfrac{168}{3} = 56$

Now we can plug this value for x in the expressions for the two unknown angle to get their value:

$B = x-5 = 56-5 = 51,\quad C = 2x-15 = 2\cdot 56-15 = 112-15 = 97$

Answer 2

You will get x as 56 and angle ABC as 51°