Question

four angle of a pentagon are 100, 175,85 and 75. find the fifth angle​

Answer 1

Given :

• Measure of four angles of pentagon :-
• First angle = 100°
• Second angle = 175°
• Third angle = 85°
• Fourth angle = 75°

To find :

• Fifth angle of the Pentagon

Concept Used :

For finding the fifth angle of the Pentagon :-

• Firstly, we will assume the fifth angle as x.
• Then add all the angles of the Pentagon and keep it equal to the sum of interior angles of the Pentagon.

To find the sum of the interior angles of the Pentagon :-

Use formula,

• Sum of interior angles of polygon = (2n - 4) × 90°

where,

• n is the number of sides of the polgyon

Solution :

Let the fifth angle of the Pentagon = x

Pentagon has 5 sides, 5 angles.

Therefore, n = 5

→ 100° + 175° + 85° + 75° + x = (2n - 4) × 90°

→ 435° + x = ((2 × 5) - 4) × 90°

→ 435° + x = (10 - 4) × 90°

→ 435° + x = 6 × 90°

→ 435° + x = 540°

→ x = 540° - 435°

→ x = 105°

The measure of the fifth angle of the Pentagon = x = 105°

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Verification :

Add all the angles of the Pentagon if they sum upto 540° then the values are right.

• First angle = 100°
• Second angle = 175°
• Third angle = 85°
• Fourth angle = 75°
• Fifth angle = 105°

Their sum :-

→ 100° + 175° + 85° + 75° + 105°

→ 540°

Sum of angles of Pentagon = 540°

Hence, verified.

Answer 2

$\huge\boxed{\texttt{\fcolorbox{black}{pink}{Answer}}}$

$\green{Let \: the \: fifth \: angle \: of \: the \: Pentagon \: = x }$

Pentagon has 5 sides, 5 angles.

Therefore, n = 5

➻ 100° + 175° + 85° + 75° + x = (2n - 4) × 90°

➻ 435° + x = ((2 × 5) - 4) × 90°

➻ 435° + x = (10 - 4) × 90°

➻ 435° + x = 6 × 90°

➻ 435° + x = 540°

➻ x = 540° - 435°

➻ x = 105°

The fifth angle of the Pentagon = x = 105°

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$\huge\boxed{\texttt{\fcolorbox{black}{pink}{Lets Verify :}}}$

Add all the angles of the Pentagon if they sum upto 540° then the values are right.

First angle = 100°

Second angle = 175°

Third angle = 85°

Fourth angle = 75°

Fifth angle = 105°

Their sum :-

→ 100° + 175° + 85° + 75° + 105°

→ 540°

Sum of angles of Pentagon = 540°

Hence, verified.

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