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Maths-

General

Easy

Question

Find the value of ‘x’ in the given figure

50°
100°
90°
120°

hint Hint:

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

The correct answer is: 90°

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

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