In the given figure, points A, B, C and D are concyclic and angle CBE = 130 degree Then / FDC is :
a) 50° (d) 30° (c) 130° (d) 80°
Answers
Answer:
A. 50°
A. 50°
A. 50°
A. 50°
A. 50°
- (C) 130°
Given :- In the given figure, points A, B, C and D are concyclic and angle CBE = 130° .
To Find :- ∠FDC = ?
Solution :-
Basic Method :-
since AE is a straight line .
→ ∠ABC + ∠CBE = 180° { Linear pair }
→ ∠ABC + 130° = 180°
→ ∠ABC = 180° - 130°
→ ∠ABC = 50°.
now, in cyclic quadrilateral ABCD,
→ ∠ADC + ∠ABC = 180° { Sum of opposite angles of a cyclic quadrilateral is equal to 180° . }
→ ∠ADC + 50° = 180°
→ ∠ADC = 180° - 50°
→ ∠ADC = 130°.
agin, FA is a straight line .
→ ∠FDC + ∠ADC = 180° { Linear pair }
→ ∠FDC + 130° = 180°
→ ∠FDC = 180° - 130°
→ ∠FDC = 50° (C) (Ans.)
Short Method :-
since AE is a straight line .
→ ∠ABC + ∠CBE = 180° { Linear pair }
→ ∠ABC + 130° = 180°
→ ∠ABC = 180° - 130°
→ ∠ABC = 50°.
now,
→ ∠FDC = ∠ABC { The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. }
therefore,
→ ∠FDC = 50° (C) (Ans.)
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