Question

The measures of exterior angles, formed by producing each side of a hexagon in order are 4x, 2x+6, 3x-1, 5x-9,x+9and2x-2

Answer 1

$hey \: mate \: here \: is \: your \: answer$

$\textbf{Given That.....}$

In A Haxagon Each Of Its Exterior Side Is Produced And Angle Formed Are 4x , 2x+6,3x-1,5x-9, X + 9 And 2x-2

Now We Need To Find Measures OF Each Exterior Angle.

$\textbf{Solution.....}$

The Exterior Angle That Are Given Are ...

$(4x) \: \: (2x + 6) \: \: ( 3x - 1) \: \: (5x - 9) \: \:( x + 9) \: \: and \: (2x - 2)$

Now We Need To Find Measures of all angle.

So For That Follow This Simple Steps ....

1 ) We know that....

$\textbf{Exterior Angle}$ Theorem States That In Any Polygon With Any Side Sum Of Their Exterior

Angle Will Always Add Upto 360°.

So Now According to this statement we have

$4x + 2x + 6 + 3x - 1 + 5x - 9 + x + 9 + 2x - 2 = 360$

So Now Open The Bracket And Compare The Like Terms ..

We Have..➡️

$4x + 2x + 3x + 5x + 2x + x + 6 - 1 - 9 + 9 - 2 = 360$

That is ➡️

$17x + 3 = 360$

Now Taking 3 To Rhs We Have ➡️

$17x = 360 - 3$

That is ➡️

$17x = 357$

Now taking 17 to RHS we have ➡️

$x = \frac{360}{17} = 21$

So Now We know the value of X

2) So Now Put This Value Of X In Each Angle .

Angle 1 = 4x ➡️ 4 × 21 = 84°

Angle 2 = 2x +6 ➡️ 2 × 21 + 6 = 48°

Angle 3 = 3x-1➡️3 × 21 -1 = 62°

Angle 4 = 5x -9➡️5 × 21 -9= 96°

Angle 5 = X + 9➡️ 21 +9 = 30°

Angle 6 = 2x- 2➡️2 × 21 - 2 = 40°

Hence The Required Answer Is .....

84 ° , 48° , 62° , 96° , 30° And 40°

$hope \: its \: help \: full$

Thought of the day.....

“I slept and I dreamed that life is all joy. I woke and I saw that life is all service. I served and I saw that service is joy.”

– Kahlil Gibran


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