The interior angles of a lexagon are 2x°, x°, x+40,110°, 130° and 160°. Find the value of the smallest angle.

Jumla ya pembe za ndani za poligoni yenye $n$ pande hutolewa na fomula $(n-2) \times 180^\circ$. Kwa heksagoni, $n=6$.

Pembe zilizopewa ni $2x^\circ$, $\frac{1}{2}x^\circ$, $(x+40)^\circ$, $110^\circ$, $130^\circ$, na $160^\circ$.

Kwanza, jumlisha vigezo vya $x$ na namba zisizo na $x$:

Toa 440 kutoka pande zote mbili:

Gawanya pande zote mbili kwa 3.5:

• Pembe ya kwanza: $2x^\circ = 2(80)^\circ = 160^\circ$
• Pembe ya pili: $\frac{1}{2}x^\circ = \frac{1}{2}(80)^\circ = 40^\circ$
• Pembe ya tatu: $(x+40)^\circ = (80+40)^\circ = 120^\circ$
• Pembe ya nne: $110^\circ$
• Pembe ya tano: $130^\circ$
• Pembe ya sita: $160^\circ$

Kulinganisha pembe zote: $160^\circ, 40^\circ, 120^\circ, 110^\circ, 130^\circ, 160^\circ$.
Pembe ndogo zaidi ni $40^\circ$.