Question

In the given figure , O is the centre of a circle and angle OAB =50° ,then angle BOD equals to?
(a) 50°
(b) 80°
(c) 100°
(d) 130°​

Answer 1

Answer:

for this question 100 degrees is the answer as 50 x 2

= 100

Answer 2

Given:

Angle OAB=50°

To find:

The angle BOD

Solution:

The required angle BOD is 100°. (Option c)

We see that since O is the circle's centre, OA, OB, and OD are the radii.

So, OA=OB=OD.

Now, in ΔAOB,

angle OAB=angle OBA (Corresponding to equal sides OB, OA)

So, angle OBA=50°

Also, angle OAB+angle OBA+angle AOB=180°

Using the values, we get

50°+50°+angle AOB=180°

100°+angle AOB=180°

Angle AOB=180°-100°

Angle AOB=80°

The line AD is straight and so the angle AOB and angle BOD form a linear pair.

Angle BOD+angle AOB=180°

Angle BOD+80°=180°

Angle BOD=180°-80°

Angle BOD=100°

Therefore, the required angle BOD is 100°.