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Class 10 Class 12

ત્રિકોણ

$bold increment bold space bold ABC$ માં, $bold m bold space bold angle bold space bold A bold space bold minus bold space bold m bold space bold angle bold space bold B bold space bold equals bold space bold 70 bold space bold અન ે bold space bold m bold space bold angle bold space bold B bold space bold minus bold space bold m bold space bold angle bold space bold C bold space bold equals bold space bold 40$ હોય, તો $bold increment bold space bold ABC$ ના તમામ ખૂણાઓનાં માપ શોધો.

જો $bold increment bold space bold ABC$ ના બહિષ્કોણ $bold angle bold space bold ACD$ નું માપ 120 છે અને તેના બે અંતઃસંમુખકોણ પૈકી કોઈ એકનું માપ 40 છે, તો $bold increment bold space bold ABC$ ના અન્ય ખૂણાનાં માપ શોધો.

નીચેની દરેક આકૃતિમાં xની કિંમત ગણો : (x દર્શાવેલ ખૂણાનું માપ દર્શાવે છે.)

આકૃતિ : 1

અહીં, $bold m bold space bold angle bold space bold BAC bold space bold plus bold space bold m bold space bold angle bold space bold BAE bold space bold equals bold space bold 180$ (રૈખિક જોડના ખૂણા)

$bold therefore bold space bold m bold space bold angle bold space bold BAC bold space bold plus bold space bold 110 bold space bold equals bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold BAC bold space bold equals bold space bold 180 bold space bold minus bold space bold 110 bold therefore bold space bold m bold space bold angle bold space bold BAC bold space bold equals bold space bold 70$

$bold m bold space bold angle bold space bold ACB bold space bold plus bold space bold m bold space bold angle bold space bold ACD bold space bold equals bold space bold 180$ (રૈખિક જોડના ખૂણા)

$bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold plus bold space bold 105 bold space bold equals bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold equals bold space bold 180 bold space bold minus bold space bold 105 bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold equals bold space bold 75$

$bold increment bold space bold ABC$ માં,

$bold m bold space bold angle bold space bold BAC bold space bold plus bold space bold m bold space bold angle bold space bold ABC bold space bold plus bold space bold m bold space bold angle bold angle bold space bold ACB bold space bold equals bold space bold 180 bold therefore bold space bold 70 bold space bold plus bold space bold x bold space bold plus bold space bold 75 bold space bold equals bold space bold 180 bold therefore bold space bold x bold space bold equals bold space bold 180 bold space bold minus bold space bold 70 bold space bold minus bold space bold 75 bold therefore bold space bold x bold space bold equals bold space bold 35$

આકૃતિ : 2

$bold m bold space bold angle bold space bold ABE bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ACB bold therefore bold space bold 105 bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ACB bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. open parentheses bold 1 close parentheses bold m bold space bold angle bold space bold ACD bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ABC bold therefore bold space bold 100 bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold angle bold space bold ABC bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. open parentheses bold 2 close parentheses$

પરિણામ (1) અને (2)નો સરવાળો લેતાં,

$bold 105 bold space bold plus bold space bold 100 bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ACB bold space bold plus bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ABC bold therefore bold space bold 205 bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space open parentheses bold m bold space bold angle bold space bold ACB bold space bold plus bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold ABC close parentheses bold therefore bold space bold 205 bold space bold equals bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold A bold space bold equals bold space bold 205 bold space bold minus bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold A bold space bold equals bold space bold 25 bold therefore bold space bold x bold space bold equals bold space bold 25$