The size of an interior angle of a regular polygon is 3x° while its exterior is (x + 20)°. Find the number of triangles that makes the polygon.

Jumla ya pembe ya ndani na pembe ya nje ya poligoni ni $180^\circ$.

$$3x^\circ + (x+20)^\circ = 180^\circ$$

$$3x + x + 20 = 180$$ $$4x + 20 = 180$$ $$4x = 180 - 20$$ $$4x = 160$$ $$x = \frac{160}{4}$$ $$x = 40$$

Pembe ya nje = $(x+20)^\circ$

$$\text{Pembe ya nje} = (40+20)^\circ = 60^\circ$$

Kwa poligoni ya kawaida, jumla ya pembe za nje ni $360^\circ$. Kwa hivyo, idadi ya pande ($n$) ni $360^\circ$ kugawanywa na pembe moja ya nje.

$$n = \frac{360^\circ}{\text{Pembe ya nje}}$$ $$n = \frac{360^\circ}{60^\circ}$$ $$n = 6$$

Poligoni ina pande 6, kwa hivyo ni heksagoni.

Idadi ya pembetatu zinazounda poligoni yenye pande $n$ ni $n-2$.

$$\text{Idadi ya pembetatu} = n - 2$$ $$\text{Idadi ya pembetatu} = 6 - 2$$ $$\text{Idadi ya pembetatu} = 4$$

Idadi ya pembetatu zinazounda poligoni ni:

$$4$$