Question - {Refer to picture attached.}
Answer of the question - (i)60°, (ii)82°.
I wanna the complete explanation of how the answer came.
Source - R.D. Sharma Mathematics Class 9 CBSE.
Step by step Explanation required! It would be okay if you don't skip any single step!
All the best! :D
Answers
Number (i) :-
We know that "The angle subtended by an arc at the centre is double the angle subtended by it at any point in remaining part of the circle". [Degree Measure Theorem]
∴ ∠AOC = 2∠APC
=> 120° = 2∠APC
=> ∠APC = 120°/2
=> ∠APC = 60°
Now, we shall use the theorem "Sum of opposite angles of any cyclic quadrilateral is 180°".
=> ∠APC + ∠ABC = 180°
=> 60 ° + ∠ABC = 180°
=> ∠ABC = 180° - 60°
=> ∠ABC = 120°
Finally :-
=> ∠DBC + ∠ABC = 180° [Linear pair]
=> x + 120° = 180°
=> x = 180° - 120°
=> x = 60°
Number (ii) :-
In ΔDAB , we will firstly calculate ∠DAB by using Angle Sum Property.
=> ∠ADB + ∠DAB + ∠DBA = 180°
=> 32° + ∠DAB + 50° = 180°
=> ∠DAB = 180°- (32° + 50°)
=> ∠DAB = 180° - 82°
=> ∠DAB = 98°
Now we will again use the theorem which we used in the last problem i.e. "Sum of opposite angles of a cyclic quadrilateral is 180°".
=> ∠DAB + ∠DCB = 180°
=> 98° + x = 180°
=> x = 180° - 98°
=> x = 82°