The angles opposite equal sides are also equal. The sum of angles in a triangle is 180. So 2x + 27 + 2x + 27 + 3x + 28 = 180.

7x + 82 = 180
7x = 98
x = 14

Now plug x into each angle to find their measures.

6 0

3 years ago

Reasoning triangle $abc$ has a perimeter of $12$ units. the vertices of the triangle are $a(x,\ 2),\ b(2,-2)$ , and $c(-1,\ 2)$

OlgaM077 [116]

hmmm let's find the distance between B and C first off.

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{-1}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BC=\sqrt{(~~-1 - 2~~)^2 + (~~2 - (-2)~~)^2} \implies BC=\sqrt{(-1 -2)^2 + (2 +2)^2} \\\\\\ BC=\sqrt{( -3 )^2 + ( 4 )^2} \implies BC=\sqrt{ 9 + 16 } \implies BC=\sqrt{ 25 }\implies BC=5$

hmmm if BC is that much, then AB + AC = 7, since AB + AC + BC = 12 which is the perimeter, Check the picture below.

6 0

2 years ago