Answer

Verified

448.5k+ views

**Hint:**: In this question we have to find out the value of $\angle BCD$. The given figure is a trapezium. A trapezium is a quadrilateral having a pair of sides parallel to each other and other pair may or may not be equal. One should know the property of trapezium and parallel line with a transversal for solving this question. Find out the value of $\angle RDE$ and then find out $\angle EDC$ and at last work out the value of $\angle DCA$.

**Complete step by step solution:**

In the given trapezium $ACDE$,

$QE\parallel RD$are parallel and $ED$is a transversal.

We know,

If $QE\parallel RD$are parallel and $ED$is transversal, then,

Sum of integer angles are supplementary i.e. ${180^\circ}$

$\therefore \angle QED + \angle RDE = {180^\circ}$ $\left[ {\angle QED = {{52}^\circ},given} \right].$

$\therefore {52^\circ} + \angle RDE = {180^\circ}$

$ \Rightarrow \angle RDE = {128^\circ}$

From the figure –

$\angle RDE + \angle RDC + \angle EDC = {360^\circ}$as it makes a complete circle.

$ \Rightarrow {128^\circ} + {126^\circ} + \angle EDC = {360^\circ}$ $\left[ {\because \angle RDC = {{126}^\circ}} \right]$

$ \angle EDC = {360^\circ} - {128^\circ} - {126^\circ} = {360^\circ} - {254^\circ} = {106^\circ}$

Again, in trapezium $ACDE$ –

$ED\parallel AB$.

$\therefore \angle EDC$and $\angle DCB$are interior angles.

$

\angle EDC + \angle DCB = {180^\circ} \\

{106^\circ} + \angle DCB = {180^\circ} \\

\Rightarrow \angle DCB = {180^\circ} - {106^\circ} = {74^\circ} \\

$

**$\therefore$The $\angle BCD$ is ${74^\circ}$. Correct option is (B).**

**Note:**The asked question was from the geometric portion so we need to have knowledge about the properties of the trapezium. In these types of questions the diagram should be clear. Read the question very carefully relating the given information to the diagram & to understand what answer they have asked for. Different rules of geometry about supplementary angles, the sum of all angles around a point is $360^\circ $should always be kept in mind while doing geometry problems otherwise you won’t be able to establish a relationship between different angles. Make sure that you don’t make a mistake in the calculation because that will bring an incorrect answer instead of having all the concepts & procedures clear in your mind.

Recently Updated Pages

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

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

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

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

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