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Maths-

General

Easy

Question

In the figure AB = AC and BC = BD. A, B, D are collinear and $angle$ CAB = 30° then $angle$ CDB=

45°
52.5°
54°
37.5°

hint Hint:

Use angle sum property

The correct answer is: 37.5°

$angle C A B equals 30 to the power of ring operator A B equals A C angle A B C equals angle A C B equals x space left parenthesis a n g l e s space f o r m e d space b y space t h e space e q u a l space s i d e s space o f space t r i a n g l e space a r e space a l s o space e q u a l right parenthesis I n space t r i a n g l e space A B C angle A B C plus angle C A B plus angle A C B equals 180 to the power of ring operator space left parenthesis a n g l e space s u m space p r o p e r t y space o f space t r i a n g l e space right parenthesis x plus 30 plus x equals 180 to the power of ring operator 2 x equals 150 to the power of ring operator x equals 75 to the power of ring operator B C equals B D space left parenthesis g i v e n right parenthesis angle B C D equals angle B D C space equals y space left parenthesis a n g l e s space f o r m e d space b y space t h e space e q u a l space s i d e s space o f space t r i a n g l e space a r e space a l s o space e q u a l right parenthesis a l s o angle C B A plus angle C B D space equals 180 to the power of ring operator space left parenthesis a n g l e space s u m space p r o p e r t y right parenthesis 75 plus C B D equals 180 to the power of ring operator angle C B D equals 105 to the power of ring operator n o w angle C B D plus angle C D B plus angle B C D equals 180 to the power of ring operator space space left parenthesis a n g l e space s u m space p r o p e r t y space o f space t r i a n g l e space right parenthesis 105 to the power of ring operator plus y plus y equals 180 to the power of ring operator y equals 180 to the power of ring operator minus 105 to the power of ring operator 2 y equals 75 to the power of ring operator y equals 75 divided by 2 y equals 37.5 to the power of ring operator angle C D B equals 37.5 to the power of ring operator$

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