Page 1 - Lesson note-7 Extra Questions Ch.10 Circle

SAI International RESIDENTIAL School
Class -IX

Mathematics

Chapter-10: Circle

Sub topic : Extra Questions.-7

Question 1:
In a cyclic quadrilateral ABCD if AB||CD and ∠B = 70⁰, find the remaining angles.
Solution:
A cyclic quadrilateral ABCD with AB||CD and B = 70⁰.
∠B + ∠C = 180⁰ (Co-interior angle)
70⁰+ ∠C = 180⁰
∠C = 110⁰
And,
=> ∠B + ∠D = 180⁰ (Opposite angles of Cyclic quadrilateral)
700 + ∠D = 180⁰
∠D = 110⁰
Again, ∠A + ∠C = 180⁰ (Opposite angles of cyclic quadrilateral)
∠A + 110⁰ = 180⁰
∠A = 70⁰

Answer: ∠A = 70⁰, ∠C = 110⁰and ∠D = 110⁰
Question 2: In a cyclic quadrilateral ABCD, if ∠A = 3(∠C). Find m ∠A.
Solution:
∠A + ∠C = 180⁰.....(1) [Opposite angles of cyclic quadrilateral]
Since ∠A = 3(∠C) (given)
From equation (1) ,3∠C + ∠C = 180⁰
Or 4∠C = 180⁰
or ∠C = 45⁰
From equation (2)
∠A = 3 x 45⁰= 135⁰

Question 3: In figure, O is the centre of the circle ∠DAB = 50°. Calculate the values of x
and y.