In Fig. 16.187, ∠BAD=78°, ∠DCF=x° and ∠DEF=y°. Find the values of x and y.
Answers
Given: ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°.
To find: values of x and y.
Solution :
Since, ABCD is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∠BAD + ∠BCD = 180°
78°+ ∠BCD = 180°
∠BCD = 180° - 78°
∠BCD = 102°
Now,
∠BCD + ∠DCF = 180°
[Linear pair]
102° + x° = 180°
x = 180° - 102°
x = 78°
Since, DCEF is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
x + y = 180°
78° + y = 180°
y = 180° - y = 78°
y = 102°
Hence, the value of x is 78° and y is 102°.
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Answer:
Step-by-step explanation:
∠BAD + ∠BCD = 180°
78°+ ∠BCD = 180°
∠BCD = 180° - 78°
∠BCD = 102°
Now,
∠BCD + ∠DCF = 180°
[Linear pair]
102° + x° = 180°
x = 180° - 102°
x = 78°
Since, DCEF is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
x + y = 180°
78° + y = 180°
y = 180° - y = 78°
y = 102°