Question

The angle of a pentagon are x,2x,x+60,x+10,x- 10. find the volume of x hence, find each of the angles

Answer 1

Appropriate Question:-

The angles of a pentagon are x, 2x, x+60, x+10, x- 10. Find the value of x and hence, find each of the angles.

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Given:-

• Angles of a pentagon = x, 2x, x+60, x+10 and x- 10.

To Find:-

• Value of x,

• Angles of the Pentagon

Property used:-

• Sum of all angles of Pentagon = 540°

Solution:-

$\sf :\implies\:x+2x+x+60+x+10+ x- 10 = 540°$

$\sf :\implies\:6x+60 = 540°$

$\sf :\implies\:6x= 540-60$

$\sf :\implies\:6x= 480$

$\sf: \implies\:x = \dfrac{480}{6}$

${\boxed{\sf{:\implies\:x= 80}}}$

Hence, The Value of x is 80.

Now,

For Angles of Pentagon:-

• ∠1 = x = 80°

• ∠2 = 2x = 2 × 80 = 160°

• ∠3 = x + 60 = 80 + 60 = 140°

• ∠4 = x + 10 = 80 + 10 = 90°

• ∠5 = x - 10 = 80 - 10 = 70°

Hence, The Angles of the Pentagon are 80°, 160°, 140°, 90° and 70°.

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More Information:-

• Sum of the interior angles of a polygon of n sides = (n – 2) × 180°.

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Answer 2

$\sf{\blue{\sf{Answer:}}}$

Explanation:

1. Given:

• The angles of a pentagon are x, (x - 10), (x + 20). (2x - 70). (2x - 44).

To Find:

• To find value of x and hence find all angles

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Note :A Pentagon having 5sides and 5 angles whose sum of all 5 angles is 540°

$\tt{x + x - 10 + x + 20 + 2x - 70 + 2x - 44 }={\blue {540}}$

Reason given above why 540??

$\tt 7x + 20 - 10 - 70 - 44 = 540=>7x+20−10−70−44=540$

$\tt 7x + 10 - 70 - 44 = 540=>7x+10−70−44=540$

$\tt 7x - 60 - 44 = 540=>7x−60−44=540$

$\tt 7x - 104 = 540=>7x−104=540$

$\tt 7x = 540 + 104 = 644=>7x=540+104=644$

$\sf x = \frac{644}{7} = 92$

$\bold{\blue{X=92°}}$

Hence ,the first angle is x=92°

ㅤㅤㅤㅤSecond angle =x-10=82°

ㅤㅤㅤㅤThird angle=x+20=112°

• Fourth angle=2x-70=2×92-70=114°

• Fifth angle=2x-44=184-44=>140°

Checking:-

$\rm {\boxed{92°+82°+112°+114°+140°=540°}}$