Question

In the given fig., O is the centre of a circle and ABE is a straight line.If angle CBE =55°, find:
1.angle ADC
2.Angle ABC
3. thevalue of x
plz answer ASAP

Answer 1

thank you for asking a good question.

Answer 2

Given:

Angle CBE=55°

To find:

i. Angle ADC

ii. Angle ABC

iii. Angle x

Solution:

The value of angle ADC is 55°, angle ABC is 125°, and x is 250°.

i. The given angle CBE is equal to 55°.

The angle in the alternate segment will be equal to this angle.

So, angle ADC=angle CBE=55°.

ii. Since the line ABE is straight, the angles CBE and ABC form a linear pair.

Angle CBE+ angle ABC=180°

Using values,

55°+angle ABC=180°

Angle ABC=125°

iii. The angle drawn at the center is twice the angle ADC.

So, angle AOC=2(angle ADC)

Angle AOC=2(55°)

Angle AOC=110°

So, the reflex angle AOC, x=360°-angle AOC

x=360°-110°

x=250°

Therefore, the value of angle ADC is 55°, angle ABC is 125°, and x is 250°.