Four interior angles of an irregular polygon are 163°, 130°, 137°, and 165° while the rest are 133° each…

Question

Four interior angles of an irregular polygon are 163°, 130°, 137°, and 165° while the rest are 133° each. Find the number of sides of the polygon.

ScanSolve AI Tutor · Accepted Answer

Hapa kuna hatua za kutatua swali la 13:

Swali la 13: Pembe nne za ndani za poligoni isiyo ya kawaida ni $163^\circ, 130^\circ, 137^\circ$ , na $165^\circ$ huku zingine zikiwa $133^\circ$ kila moja. Tafuta idadi ya pande za poligoni.

Andika fomula ya jumla ya pembe za ndani za poligoni yenye pande $n$ .
Jumla ya pembe za ndani za poligoni ni $S = (n-2) \times 180^\circ$ .
Kokotoa jumla ya pembe nne zilizotolewa.
Jumla ya pembe nne = $163^\circ + 130^\circ + 137^\circ + 165^\circ = 595^\circ$ .
Eleza jumla ya pembe zilizobaki.
Ikiwa kuna pande $n$ , basi kuna pembe $n$ . Pembe nne zimetolewa, kwa hivyo pembe zilizobaki ni $n-4$ . Kila moja ya pembe hizi ni $133^\circ$ .
Jumla ya pembe zilizobaki = $(n-4) \times 133^\circ$ .
Sawazisha jumla ya pembe zote na fomula ya jumla ya pembe za ndani.
$595^\circ + (n-4) \times 133^\circ = (n-2) \times 180^\circ$
Panua na kurahisisha mlinganyo.
$595 + 133n - (4 \times 133) = 180n - (2 \times 180)$ $595 + 133n - 532 = 180n - 360$ $63 + 133n = 180n - 360$
Tatua kwa $n$ .
Kusanya maneno ya $n$ upande mmoja na nambari upande mwingine.
$360 + 63 = 180n - 133n$ $423 = 47n$ $n = \frac{423}{47}$ $n = 9$
Idadi ya pande za poligoni ni 9.

Four interior angles of an irregular polygon are 163°, 130°, 137°, and 165° while the rest are 133° each. Find the number of sides of the polygon.

Answer

Step-by-step solution

Andika fomula ya jumla ya pembe za ndani za poligoni yenye pande $n$ .

Kokotoa jumla ya pembe nne zilizotolewa.

Eleza jumla ya pembe zilizobaki.

Sawazisha jumla ya pembe zote na fomula ya jumla ya pembe za ndani.

Panua na kurahisisha mlinganyo.

Tatua kwa $n$ .

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Four interior angles of an irregular polygon are 163°, 130°, 137°, and 165° while the rest are 133° each. Find the number of sides of the polygon.

Answer

Step-by-step solution

Andika fomula ya jumla ya pembe za ndani za poligoni yenye pande nnn.

Kokotoa jumla ya pembe nne zilizotolewa.

Eleza jumla ya pembe zilizobaki.

Sawazisha jumla ya pembe zote na fomula ya jumla ya pembe za ndani.

Panua na kurahisisha mlinganyo.

Tatua kwa nnn.

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Andika fomula ya jumla ya pembe za ndani za poligoni yenye pande $n$ .

Tatua kwa $n$ .