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Maths-

General

Easy

Question

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

$45^{\circ}$
${52.5}^{\circ}$
$54^{\circ}$
${37.5}^{\circ}$

The correct answer is: $37.5 to the power of ring operator end exponent$

$angle C B A plus angle C B D equals 180 to the power of ring operator space left parenthesis s u p p l e m e n t a r y space a n g l e s space a r e space e q u a l right parenthesis angle C B D equals 180 to the power of ring operator minus 130 to the power of ring operator angle C B D equals 50 to the power of ring operator space l e t apostrophe s space angle C D B space equals x space space space t h e n space angle B C D space w i l l space a l s o space b e space x space left parenthesis a n g l e s space f o r m e d space b y space e q u a l space s i d e s space i n space t r i a n g l e s space a r e space a l s o space e q u a l right parenthesis space space angle C B D plus angle B C D plus angle C D B space equals 180 to the power of ring operator 50 to the power of ring operator plus x plus x equals 180 to the power of ring operator 50 to the power of ring operator plus 2 x equals 180 to the power of ring operator 2 x equals 180 to the power of ring operator minus 50 to the power of ring operator x equals 65 to the power of ring operator angle C D B equals 65 to the power of ring operator$

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