Question

1. The angles of a pentagon are x, (x - 10), (x + 20). (2x - 70). (2x - 44). Find
the value of x and hence find the measure of all the angles of pentagon.​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

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°

$\bold{x + x - 10 + x + 20 + 2x - 70 + 2x - 44 }= {\red{540}}$

Reason given above why 540??

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

$= > 7x + 10 - 70 - 44 = 540$

$= > 7x - 60 - 44 = 540$

$= > 7x - 104 = 540$

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

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

$\huge\bold{\red{X=92°}}$

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°

Check:-

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

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

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

ㅤㅤㅤㅤㅤ

ㅤㅤㅤㅤㅤㅤ

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

$\bold{x + x - 10 + x + 20 + 2x - 70 + 2x - 44 }= {\red{540}}$

Reason given above why 540??

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

$= > 7x + 10 - 70 - 44 = 540$

$= > 7x - 60 - 44 = 540$

$= > 7x - 104 = 540$

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

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

$\huge\bold{\red{X=92°}}$

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°

Check:-

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