In a cyclic quadrilateral ABCD,angle A : angl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In a cyclic quadrilateral,the sum of opposite angles is $180^{\circ}$.Given $\angle A : \angle C = 4 : 5$,let $\angle A = 4x$ and $\angle C = 5x$.

Vedclass · Accepted Answer

$\angle A = 80^{\circ}, \angle B = 75^{\circ}, \angle C = 100^{\circ}, \angle D = 105^{\circ}$

Vedclass · Answer

(D) In a cyclic quadrilateral,the sum of opposite angles is $180^{\circ}$.Given $\angle A : \angle C = 4 : 5$,let $\angle A = 4x$ and $\angle C = 5x$.Since $\angle A + \angle C = 180^{\circ}$,we have $4x + 5x = 180^{\circ} \Rightarrow 9x = 180^{\circ} \Rightarrow x = 20^{\circ}$.Thus,$\angle A = 4(20^{\circ}) = 80^{\circ}$ and $\angle C = 5(20^{\circ}) = 100^{\circ}$.Given $\angle B : \angle D = 5 : 7$,let $\angle B = 5y$ and $\angle D = 7y$.Since $\angle B + \angle D = 180^{\circ}$,we have $5y + 7y = 180^{\circ} \Rightarrow 12y = 180^{\circ} \Rightarrow y = 15^{\circ}$.Thus,$\angle B = 5(15^{\circ}) = 75^{\circ}$ and $\angle D = 7(15^{\circ}) = 105^{\circ}$.Therefore,the angles are $\angle A = 80^{\circ}, \angle B = 75^{\circ}, \angle C = 100^{\circ}, \angle D = 105^{\circ}$.

In a cyclic quadrilateral $ABCD$,$\angle A : \angle C = 4 : 5$ and $\angle B : \angle D = 5 : 7$. Find all the angles of $ABCD$.

Similar Questions

Two equal chords $AB$ and $CD$ of a circle when produced intersect at a point $P$. Prove that $PB = PD$.

$AB$ and $AC$ are two chords of a circle with centre $P$. If the bisector of $\angle BAC$ passes through the centre $P$,prove that $AB = AC$.

Write True or False and justify your answer in each of the following:
If $A, B, C$ and $D$ are four points such that $\angle BAC = 45^{\circ}$ and $\angle BDC = 45^{\circ}$,then $A, B, C, D$ are concyclic.

$O$ is the circumcentre of the triangle $ABC$ and $D$ is the mid-point of the base $BC$. Prove that $\angle BOD = \angle A$.

In the figure,$\angle ADC = 130^{\circ}$ and chord $BC = $ chord $BE$. Find $\angle CBE$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module