Question

in the adjoining figure angle AOC=100 degree calculate angle ABC reflex angle AOC and Angle ADC​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

Angle AOC=100°

To find:

i. Angle ABC

ii. Reflex angle AOC

iii. Angle ADC

Solution:

The measure of angle ABC, reflex angle AOC, and angle ADC is 50°, 260°, and 130°, respectively.

We can find the angles by following the given process-

i. We know that the angle made at the centre from two points is double the angle made at any point on the circumference from the same points.

So, angle AOC is twice the angle ABC.

Angle AOC=2×angle ABC

100°=2×angle ABC

Angle ABC=100/2=50°

ii. Now, the angle AOC and reflex angle AOC form a complete angle.

So, the sum of angle AOC and reflex angle AOC is 360°.

Angle AOC+Reflex angle AOC=360°

On putting the values,

100°+ reflex angle AOC=360°

Reflex angle AOC=360°-100°

Reflex angle AOC=260°

iii. We know that the quadrilateral ABCD is cyclic.

The opposite angles of ABCD are supplementary.

So, angle ABC+angle ADC=180°

Angle ABC=50°

50°+angle ADC=180°

Angle ADC=180°-50°

Angle ADC=130°

Therefore, the measure of angle ABC, reflex angle AOC, and angle ADC is 50°, 260°, and 130°, respectively.