# The exterior angle of a regular polygon is 2x, and the interior angle is 4x.Find the measure of one interior and exterior angle.

The exterior angle of a regular polygon is 2x, and the interior angle is 4x.Find the measure of one interior and exterior angle.

### 1 thought on “The exterior angle of a regular polygon is 2x, and the interior angle is 4x.Find the measure of one interior and exterior angle.”

\frac{1}{x\:+\:4}\:+\:\frac{1}{2}\:=\:\frac{1}{x\:+\:4}x+41+21=x+41

\frac{2\:+\:(x\:+\:4)}{2(x\:+\:4}\:=\:\frac{1}{x\:+\:4}2(x+42+(x+4)=x+41

\frac{6\:+\:x}{2x\:+\:8}\:=\:\frac{1}{x\:+\:4}2x+86+x=x+41

\red{On\:cross\:multiplying\:=}Oncrossmultiplying=

(6\:+\:x)(x\:+\:4)\:=\:2x\:+\:8(6+x)(x+4)=2x+8

\blue{Opening\:brakets\:=}Openingbrakets=

6x\:+24\:+\:x^{2}\:+\:4x\:=\:2x\:+\:86x+24+x2+4x=2x+8

x^{2}\:+\:10x\:+\:24\:=\:2x\:+\:8×2+10x+24=2x+8

x^{2}\:+\:10x\:-\:2x+\:24\:-\:8\:=\:0x2+10x−2x+24−8=0

x^{2}\:+\:8x\:+\:16\:=\:0x2+8x+16=0

x^{2}\:+\:4x\:+\:4x\:+\:16\:=\:0x2+4x+4x+16=0

x(x\:+\:4)\:+\:4(x\:+\:4)\:=\:0x(x+4)+4(x+4)=0

(x\:+\:4)\:+\:(x\:+\:4)\:=\:0(x+4)+(x+4)=0

\green{Therefore\:,}Therefore,

x\:=\:-4\:,\:-4x=−4,−4

-4\:=\:\green{non\:extraneous\:variable}−4=nonextraneousvariable

Step-by-step explanation:

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