The sum of the interior angles of an n-sided polygon is 720°. Find the value of n and hence deduce the name…

Question

The sum of the interior angles of an n-sided polygon is 720°. Find the value of n and hence deduce the name of the polygon

ScanSolve AI Tutor · Accepted Answer

Haya, hebu tutatue swali hili la poligoni.

Topic: Poligoni na Jumla ya Pembe za Ndani

Andika fomula ya jumla ya pembe za ndani za poligoni.
Jumla ya pembe za ndani za poligoni yenye pande $n$ hutolewa na fomula:
$S = (n - 2) \times 180^\circ$
Weka mlinganyo kwa kutumia jumla uliyopewa.
Tunapewa kuwa jumla ya pembe za ndani ni $720^\circ$ .
$720^\circ = (n - 2) \times 180^\circ$
Tatua kwa $n$ .
Gawanya pande zote mbili kwa $180^\circ$ :
$\frac{720^\circ}{180^\circ} = n - 2$ $4 = n - 2$
Ongeza 2 kwa pande zote mbili:
$4 + 2 = n$ $n = 6$
Thamani ya $n$ ni $\boxed{6}$ .
Bainisha jina la poligoni.
Poligoni yenye pande 6 inaitwa heksagoni.
Jina la poligoni ni $\boxed{\text{heksagoni}}$ .

The sum of the interior angles of an n-sided polygon is 720°. Find the value of n and hence deduce the name of the polygon