The angles of a triangle are 2x, (2x+1), and (2x+13). Find all the angles?

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Answer 1 · 2018-06-19T08:09:28

${(\frac{166}{3})}^{\circ}, {(\frac{169}{3})}^{\circ}, {(\frac{205}{3})}^{\circ}$ $color(blue)((166/3)^@,(169/3)^@,(205/3)^@$

The sum of the interior angles of a triangle is $180^{\circ}$ $180^@$

$:.$

$2x+(2x+1)+(2x+13)=180$

$6x+14=180$

$6x=180-14=166$

$x=166/6=83/3$

So the angles are:

$2x=2(83/3)=color(blue)((166/3)^@$

$(2x+1)=(2(83/3)+1)=color(blue)((169/3)^@$

$(2x+13)=(2(83/3)+13)=color(blue)((205/3)^@$