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Maths-

General

Easy

Question

In figure, AB = AC, $angle$ A = 48° and $angle$ ACD = 18°. Then

BC > CD
BC = CD
BC < CD
cannot decide

The correct answer is: BC = CD

$A B equals A C space left parenthesis g i v e n right parenthesis s o angle A B C equals angle A C B space equals x space left parenthesis a n g l e s space f o r m e d space b y space e q u a l space s i d e s space o f space a space t r i a n g l e space a r e space a l s o space e q u a l space a n d space v i c e space v e r s a right parenthesis space I n space t r i a n g l e space A B C comma space angle C A B plus angle A B C plus angle A C B equals 180 space left parenthesis A n g l e space s u m space p r o p e r t y space o f space a space t r i a n g l e right parenthesis 48 to the power of ring operator plus x plus x equals 180 to the power of ring operator 48 to the power of ring operator plus 2 x equals 180 to the power of ring operator 2 x equals 132 to the power of ring operator x equals 66 to the power of ring operator A l s o space i n space t r i a n g l e space A C D angle C D B equals angle A C D plus angle D A C space left parenthesis e x t e r i o r space a n g l e space i s space e q u a l space t o space t h e space s u m space o f space t w o space o p p o s i t e space i n t e r i o r space a n g l e s right parenthesis angle C D B equals 48 to the power of ring operator plus 18 to the power of ring operator angle C D B equals 66 to the power of ring operator angle C D B equals angle A B C t h e r f o r e space w e space c a n space s a y space B C equals B D space left parenthesis a n g l e s space f o r m e d space b y space e q u a l space s i d e s space o f space a space t r i a n g l e space a r e space a l s o space e q u a l space a n d space v i c e space v e r s a right parenthesis$

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