Remembering Isosceles

The information $5x+2$ is not needed in the solution. Let $a$ be the measure of one of its base angle then

$a+a+36=180$

$2a=144$

$\boxed{a=72^\circ}$

Since we know that the angles of a triangle sum to 180°, we can solve this by writing an equation and solving for x.

$2(5x+2)\quad +\quad 36\quad =\quad 180\\ \\ 10x\quad +\quad 4\quad +\quad 36\quad =\quad 180\\ \\ 10x\quad +\quad 40\quad =\quad 180\\ \\ 10x\quad =\quad 140\\ \\ x\quad =\quad 14\\ \\ Now\quad to\quad find\quad the\quad base\quad angle:\\ \\ 2(5(14) + 2)\quad =\quad \boxed { 72 }$