Question

6) The four angles of a pentagon are 40°, 75°, 125°, and 135º. The measure of the fifth angle is __*

a) 165°
b) 170°
c) 160°
d) 175°​

Answer 1

Answer:

165 yes

Step-by-step explanation:

Answer 2

Answer:

$\huge\mathfrak\red {Answer}$

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ɢɪᴠᴇɴ :-

measure of the four angles of polygon :-

40° , 75° , 125° and 135°

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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.

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