求出下列图形中x的值(1)根据图1,列方程,得 解得$x=$ ;(2)根据图2,列方程,得 解得$x=$ .
的有关信息介绍如下:【答案】
$\left(1\right)$$2{x}^{\circ }+{x}^{\circ }+{90}^{\circ }+{120}^{\circ }+{150}^{\circ }={540}^{\circ }$,$60$;
$\left(2\right)$${360}^{\circ }-\left({75}^{\circ }+{120}^{\circ }+{80}^{\circ }\right)={x}^{\circ }$,$95$.
【解析】
$\left(1\right)$图$1$是五边形,其内角和为$\left(5-2\right)\times {180}^{\circ }={540}^{\circ }$,
$\therefore $列方程,得$2{x}^{\circ }+{x}^{\circ }+{90}^{\circ }+{120}^{\circ }+{150}^{\circ }={540}^{\circ }$,
合并同类项,得$3{x}^{\circ }+{360}^{\circ }={540}^{\circ }$,
移项、合并同类项得$3{x}^{\circ }={180}^{\circ }$,
解得:$x=60$;
$\left(2\right)$图$2$是四边形,其内角和为$\left(4-2\right)\times {180}^{\circ }={360}^{\circ }$,
$\therefore $列方程,得${360}^{\circ }-\left({75}^{\circ }+{120}^{\circ }+{80}^{\circ }\right)+{x}^{\circ }={180}^{\circ }$,
合并同类项,得${360}^{\circ }-2{75}^{\circ }+{x}^{\circ }={180}^{\circ }$,
解得:$x=95$.
故答案为:$\left(1\right)$$2{x}^{\circ }+{x}^{\circ }+{90}^{\circ }+{120}^{\circ }+{150}^{\circ }={540}^{\circ }$,$60$;
$\left(2\right)$${360}^{\circ }-\left({75}^{\circ }+{120}^{\circ }+{80}^{\circ }\right)={x}^{\circ }$,$95$.