Question

A circle with center O and points A, B, C, D. Angle AOC = 100 degree. find angle ADC and angle ABC​

Answer 1

Answer:

We know that the angle subtended by an arc is twice the angle subtended by it on the circumference From the figure we know that ∠AOC = 100o So we get ∠AOC = 2 ∠ADC It can be written as ∠ADC = ½ ∠AOC By substituting the values ∠ADC = ½ (100o) So we get ∠ADC = 50o We know that the opposite angles of a cyclic quadrilateral are supplementary It can be written as ∠ADC + ∠ABC = 180o By substituting the values 50o + ∠ABC = 180o On further calculation ∠ABC = 180o – 50o By subtraction ∠ABC = 130o Therefore, ∠ADC = 50o and ∠ABC = 130o.Read more on Sarthaks.com - https://www.sarthaks.com/728074/the-given-figure-the-centre-the-given-circle-and-measure-arc-abc-100-determine-adc-and-abc

Answer 2

Step-by-step explanation:

We know that the angle subtended by an arc is twice the angle subtended by it on the circumference.

From the figure we know that ∠AOC = 100

So we get ∠AOC = 2 ∠ADC

It can be written as ∠ADC = ½ ∠AOC

By substituting the values ∠ADC = ½ (100)

So we get ∠ADC = 50

We know that the opposite angles of a cyclic quadrilateral are supplementary

It can be written as

∠ADC + ∠ABC = 180

By substituting the values

50 + ∠ABC = 180

On further calculation

∠ABC = 180 – 50

By subtraction

∠ABC = 130

Therefore, ∠ADC = 50 and ∠ABC = 130.