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ત્રિકોણ

bold increment bold space bold ABCમ ાં bold space bold BE with bold bar on top bold space bold perpendicular bold space bold AC with bold bar on top bold space bold comma bold space bold D bold space bold element of bold space bold BC with bold bar on top

કે જેથી B – D – C. જો

bold m bold space bold angle bold space bold EBC bold space bold equals bold space bold 40 bold comma bold space bold m bold space bold angle bold space bold DAC bold space bold equals bold space bold 30 bold comma bold space bold ત ો bold space bold m bold space bold angle bold space bold BCE

શોધો તથા

bold m bold space bold angle bold space bold ADC

શોધો.

bold increment bold space bold ABC

ના ખૂણાઓનાં માપ 2 : 3 : 5ના પ્રમાણમાં હોય, તો 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.

$bold increment bold space bold ABCમ ાં bold space bold angle bold space bold ACD$ એ બહિષ્કોણ છે.

$bold m bold space bold angle bold space bold ACD bold space bold equals bold space bold 120$ છે.

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

$bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold plus bold space bold 120 bold space bold equals bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold equals bold space bold 180 bold space bold minus bold space bold 120 bold therefore bold space bold m bold space bold angle bold space bold ACB bold space bold equals bold space bold 60$

અર્થાત્ $bold increment bold space bold ABCમ ાં bold space bold m bold space bold angle bold space bold C bold space bold equals bold space bold 60$ છે.

હવે, $bold increment bold space bold ABC$ માં,

$bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold B bold space bold plus bold space bold m bold space bold angle bold space bold C bold space bold equals bold space bold 180 bold therefore bold space bold 40 bold space bold plus bold space bold m bold space bold angle bold space bold B bold space bold plus bold space bold m bold space bold angle bold space bold 60 bold space bold equals bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold B bold space bold plus bold space bold 100 bold space bold equals bold space bold 180 bold therefore bold space bold m bold space bold angle bold space bold B bold space bold equals bold space bold 180 bold space bold minus bold space bold 100 bold therefore bold space bold m bold space bold angle bold space bold B bold space bold equals bold space bold 80$

$bold therefore bold space bold increment bold space bold ABC$ ના બાકીના બે ખૂણાઓનાં માપ 80 અને 60 છે.

$bold increment bold space bold ABC$ 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.

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

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