Answer

Verified

349.5k+ views

**Hint:**In this problem, we have to find the value of x in the given diagram. We should first analyse the given diagram. We are also given that BC = CD, whose angle will also be equal. We can then use the angle sum property and find and find the value of one of the angles. We can see that in the first circle AEBD is a cyclic quadrilateral, then the opposite angles will be supplementary, we can use these properties and find the value of the required angle.

**Complete step by step answer:**

Here we have to find the value of x from the given diagram.

We can see that, in triangle DBC, we are given that \[\angle DCB={{50}^{\circ }}\] and CD = CB, we can now write it as,

\[\Rightarrow \angle CDB=\angle CBD\] …… (1)

By angle sum property, we can write it as,

\[\Rightarrow \angle DCB+\angle DBC+\angle CDB={{180}^{\circ }}\]

From (1), we can write as

\[\begin{align}

& \Rightarrow 2\angle CDB={{180}^{\circ }}-{{50}^{\circ }} \\

& \Rightarrow \angle CDB={{65}^{\circ }}.....(2) \\

\end{align}\]

We can see that, in the first circle AEBD is a cyclic quadrilateral, then opposite angles are supplementary.

We can now write it as,

\[\Rightarrow \angle EAB+\angle EDB={{180}^{\circ }}\]

From the diagram, we can also write the above step as,

\[\begin{align}

& \Rightarrow \angle EAB+{{180}^{\circ }}-\angle CDB={{180}^{\circ }} \\

& \Rightarrow \angle EAB=\angle CDB \\

\end{align}\]

From (2), we can write it as,

\[\Rightarrow \angle EAB=\angle CDB={{65}^{\circ }}\]

The value of x is \[{{65}^{\circ }}\].

**Therefore, the answer is option D. \[{{65}^{\circ }}\]**

**Note:**We should always remember that the supplementary angles are angles which sums up to give \[{{180}^{\circ }}\]. We should also know that if the first circle is a cyclic quadrilateral, then opposite angles are supplementary. We should know that angle sum property is the sum of the triangle equals \[{{180}^{\circ }}\].

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers