Math, asked by harryStyles1743, 11 months ago

In Fig. 16.187, ∠BAD=78°, ∠DCF=x° and ∠DEF=y°. Find the values of x and y.

Attachments:

Answers

Answered by nikitasingh79
8

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°.

HOPE THIS ANSWER WILL HELP YOU…..

 

Similar questions :

ABCD is a cyclic quadrilateral in which: (i) BC||AD, ∠ADC=110° and ∠BAC=50°. Find ∠DAC. (ii) ∠DBC=80° and ∠BAC=40° Find ∠BCD. (iii) ∠BCD=100° and ∠ABD=70°. Find ∠ADB.

https://brainly.in/question/15910505

 

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA=ED. Prove that:

(i) AD||BC (ii) EB=EC

https://brainly.in/question/15910496

Answered by Anonymous
5

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°

Similar questions