Question

the ratio between the angle of the quadrilateral is 4 : 5 :7 : 8 find the angle of the quadrilateral​

Answer 1

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ʀᴀᴛɪᴏ ᴏғ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇɪʀ ᴀɴɢʟᴇs = 4:5:7:8

ʟᴇᴛ ᴛʜᴇɪʀ ᴄᴏᴍᴍᴏɴ ʀᴀᴛɪᴏ ʙᴇ x

<1 = 4x

<2 = 5x

<3 = 7x

<4 = 8x

ʙʏ ᴜsɪɴɢ ᴀɴɢʟᴇ sᴜᴍ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ :-

<1 + <2 + <3 + <4 = 360°

4x + 5x + 7x + 8x = 360°

24x = 360°

x = 360° / 24

x = 15°

<1 = 4x = 4(15°) = 60°

<2 = 5x = 5(15°) = 75°

<3 = 7x = 7(15°) = 105°

<4 = 8x = 8(15°) = 120°