Question

the 4 angles of a pentagon are 40,75,125 and 135 degrees respectively then the measure of the 5th angle is
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Answer 1

Step-by-step explanation:

ɢɪᴠᴇɴ :-

measure of the four angles of polygon :-

40° , 75° , 125° and 135°

\:

ᴛᴏ ғɪɴᴅ :-

measure of fifth angle of the polygon.

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ :-

sum of the measure of all angles of a polygon is

=> 540°

[ angle 1 + angle 2 + angle 3 + angle 4 + angle 5 = 540° ]

\:

ʟᴇᴛ's ғɪɴᴅ :-

let the unknown angle of the polygon be x .

sum of all angles :-

=> 40 + 75 + 125 + 135 + x = 540°

=> 115 + 260 + x = 540°

=> 375 + x = 540°

=> x = 540 - 375

=> x = 165°

\:

sᴏʟᴜᴛɪᴏɴ :-

thus , the measure of the fifth angle of the polygon is 165 degrees.

Answer 2

Given:-

• Four angles of Pentagon are 40° , 75° , 125° and 135° respectively.

To find :-

• Fifth angle of Pentagon.

$\sf\blue{Solution:-}$

Let the fifth angle of Pentagon be 'x°'.

We know that,

Sum of all interior angles of Pentagon is 540°.

So,

$\implies \sf 40° + 75° + 125° +x° + 135° = 540° \\ \implies \sf375° + x° = 540° \\ \implies \sf \: x° = 540° - 375° \\ \implies \sf \: x = 165°$

Hence, Fifth angle is 165°.

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More information:-

• Pentagon is closed figure , which consists of five angles and five sides.
• It's all interior angles sum is 540°.