Question

In the figure the central angle of a circle is O if BOD= 124°, then find the value of x​

Answer 1

Step-by-step explanation:

Given that:

In the figure the central angle of a circle is O if BOD= 124°, then find the value of x

To find:

$\angle \: x$

Solution:

BD is a chord,which subtends 124° angle on the center of circle

Other angle at O is

360°-124°=236°(because complete angle is 360°)

As shown in attachment.

Thus,

$\angle \: BCD = \frac{236}{2} \\ \\ \angle \: BCD= 118°$

[If a chord subtends theta angle at center of circle,then it subtends half of theta in the remaining part of center]

Now,

BCE is a line.

Sum of all angles on a straight line is 180°

$\angle \: BCD + \angle \: x = 180° \\ \\ 118° + \angle \: x = 180° \\ \\ \angle \: x = 180° - 118° \\ \\ \angle \: x = 62°$

Thus,

$\bold{\angle \: x = 62°}$

Hope it helps you.