图中显示了一个五边形。 其中三个内角各为 100°。 它的一个外角是 50°。 求 $x$ 的值。 答案 $x$ = ...

1. Find the interior angle corresponding to the given exterior angle.

The exterior angle and the interior angle at that vertex form a straight line.

$\text{interior angle} = 180^\circ - 50^\circ = 130^\circ$

2. Use the sum of interior angles of a pentagon to find $x$.

Sum of interior angles of a pentagon:

$(5-2)\times 180^\circ = 540^\circ$

So,

$100^\circ+100^\circ+100^\circ+130^\circ+x=540^\circ$

$x=540^\circ-430^\circ=110^\circ$