English

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

Advertisements
Advertisements

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
Advertisements

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.
shaalaa.com
  Is there an error in this question or solution?
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

RELATED QUESTIONS

Prove that ‘Opposite angles of a cyclic quadrilateral are supplementary’.


A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.


In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.


ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.


If the non-parallel sides of a trapezium are equal, prove that it is cyclic.


Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.


ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.


The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?


Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90°-A, 90° − `1/2 A, 90° − 1/2 B, 90° − 1/2` C.


Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals. 


ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.


Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.


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


In the given figure, ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.


ABCD is a cyclic quadrilateral. M (arc ABC) = 230°. Find ∠ABC, ∠CDA, and ∠CBE.


If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.


In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.


If non-parallel sides of a trapezium are equal, prove that it is cyclic.


ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×