Question

A B C D are points on the circle with centre O, D= 40°.what is the measure of <AOC and < ABC​

Answer 1

Step-by-step explanation:

given :

• A B C D are points on the circle with centre O, D= 40°.what is the measure of <AOC and < ABC

to find :

• what is the measure of <AOC and < ABC

solution :

• the answer is 60 degree

Answer 2

Given :- A B C D are points on the circle with centre O, ∠D = 40° .

To Find :- The measure of ∠AOC and ∠ABC ?

Solution :-

→ ∠ADC = 40° { given }

So,

→ ∠AOC = 2•∠ADC { The angle at the centre is double the angle at the circumference . }

then,

→ ∠AOC = 2 × 40°

→ ∠AOC = 80° (a) (Ans.)

now, in cyclic quadrilateral ABCD,

→ ∠ADC = 40° { given }

→ ∠ADC + ∠ABC = 180° { The sum of the opposite angles of a cyclic quadrilateral is 180° . }

→ 40° + ∠ABC = 180°

→ ∠ABC = 180° - 40°

→ ∠ABC = 140° (b) (Ans.)

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