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Maths-

General

Easy

Question

In given figure $stack A B with rightwards arrow on top equals stack A C with bar on top$ and $stack B C with bar on top equals stack C D with bar on top comma$ if $B A C equals 80 to the power of ring operator end exponent blank$ then find $∣ C D B$

15°
25°
20°
30°

The correct answer is: 20°

$I n space t r i a n g l e space A B C angle B A C equals 80 to the power of ring operator A c c space t o space a n g l e space s u m space p r o p e r t y angle A B C plus angle A C B plus angle B A C equals 180 to the power of ring operator S I n c e space A B equals A C angle A B C equals angle A C B thin space left parenthesis a n g l e s space f o r m e d space n y space e q u a l space s i d e s space o f space t r i a n g l e space a r e space a l s o space e q u a l right parenthesis L e t space angle A B C equals x equals angle A C B 80 to the power of ring operator plus x plus x equals 180 to the power of ring operator 2 x equals 100 to the power of ring operator x equals 50 to the power of ring operator angle B C D equals angle B A C plus angle A B C space left parenthesis e x t e r i o r space a n g l e space i s space e q u a l space t o space t h e space s u m space o f space b o t h space o p p o s i t e space i n t e r i o r space a n g l e s right parenthesis angle B C D equals 80 to the power of ring operator plus 50 to the power of ring operator angle B C D equals 130 to the power of ring operator A l s o space i n space t r i a n g l e space B C D B C equals C D t h e r e f o r e space angle C D B equals angle C B D space left parenthesis a n g l e s space f o r m e d space n y space e q u a l space s i d e s space o f space t r i a n g l e space a r e space a l s o space e q u a l right parenthesis angle C B D equals angle C D B equals x angle B C D plus angle C D B plus C B D equals 180 to the power of ring operator 130 to the power of ring operator plus x plus x equals 180 to the power of ring operator 2 x equals 50 to the power of ring operator x equals 25 to the power of ring operator angle C D B equals 25 to the power of ring operator$

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