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

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Questions

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

In the figure, find the value of angles x and y.

Sum
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Solution

We have to find the value of x and y.

Since ABCD is a cyclic quadrilateral.

∠A + angle BCD = 180° (Opposite angle of a cyclic quadrilateral are supplementary)

Step 1: 

∠BAD + ∠BCD = 180°

Given ∠BAD = 78°, we can find ∠BCD

78° + ∠BCD = 180°

∠BCD = 180° −  78°

∠BCD = 102°

Step 2: 

∠BCD + x = 180°
102° + x = 180°
x = 180° − 102°
x = 78°
Step 3: 
x + y = 180°
Substitute the value of x 
78° + y = 180°
y = 180° −  78°
y = 102°
The value of x is 78°, and the value of y is 102.
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Chapter 15: Circles - Exercise 15.5 [Page 102]

APPEARS IN

R.D. Sharma Mathematics [English] Class 9
Chapter 15 Circles
Exercise 15.5 | Q 15 | Page 102
Nootan Mathematics [English] Class 10 ICSE
Chapter 15 Circles
Exercise 15A | Q 28. | Page 333

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