Q. 355.0( 1 Vote )

# In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If ∠CBE = 100°, then ∠CDF = ?

A. 100^{o}

B. 80^{o}

C. 130^{o}

D. 90^{o}

Answer :

Given: ∠CBE = 100°

Here,

∠ABE = ∠ABC + ∠CBE

180° = ∠ABC + 100°

∠ABC = 180° – 100° = 80°

We know that,

In a cyclic quadrilateral opposite angles are supplementary

∴ ∠ABC + ∠ADC = 180°

80° + ∠ADC = 180°

∠ADC = 180° – 80° = 100°

Here,

∠ADF = ∠ADC + ∠CDF

180° = 100° + ∠CDF

∠CDF = 180° – 100° = 80°

∴ ∠CDF = 80°

Rate this question :

In Fig. 16.195, *ABCD* is a cyclic quadrilateral in which ∠*BAD*=75°, ∠*ABD*=58° and ∠*ADC*=77°, *AC* and *BD* intersect at *P.* Then, find ∠*DPC*.

RD Sharma - Mathematics

In the given figure, is a quadrilateral in which and Show that the points lie on a circle.

RS Aggarwal & V Aggarwal - Mathematics

In the given figure, and

Find the values of and

RS Aggarwal & V Aggarwal - Mathematics

*PQRS* is a cyclic quadrilateral such that *PR* is a diameter of the circle. If ∠*QPR*=67° and ∠*SPR*=72°, then ∠*QRS*=

In Fig. 16.194, two congruent circles with centres *O* and *O’* intersect at *A* and *B*. If ∠*AO’B*=50°, then find ∠*APB*.

RD Sharma - Mathematics

*ABCD* is a cyclic quadrilateral such that ∠*ADB* =30° and ∠*DCA* =80°, then ∠*DAB* =

In the given figure, is the center of the given circle and measure of arc is 100°. Determine and

RS Aggarwal & V Aggarwal - Mathematics

is a rectangle. Prove that the center of the circle through is the point of intersection of its diagonals.

RS Aggarwal & V Aggarwal - MathematicsProve that the circles described with the four sides of a rhombus, as diameters, pass through the point of intersection of its diagonals.

RS Aggarwal & V Aggarwal - Mathematics