Find the measure of angle ABC

Question

asked Jul 14, 2019 188k views

2 Answers

Dummdidumm · Answer 1 · 2019-07-19T11:00:38+0000

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:

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