Question

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

Answer 1

$\huge\mathfrak\pink{Answer:}$

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★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.

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Hope it helps you ✌

Answer 2

Answer:

Given -

• 1st angle = 40°
• 2nd angle = 75°
• 3rd angle = 125°
• 4th angle = 135°

To find -

• Measure of 5th angle.

Solution -

Let the fifth angle be x.

As we know that the sum of all angles of a pentagon is 540.

Then,

Sum of all angles -

40° + 75° + 125° + 135° + x = 540°

→ 375° + x = 540°

→ x = 540 - 375

→ x = 165 °

Therefore, the measure of fifth angle is 165°.