Answer

Verified

420.3k+ views

**Hint**: In this question we have to find the value of $ x $ . To find the value of $ x $ we will use the sum of all interior angles of a triangle property and straight angle or straight-line definition. By using these properties, we can find the value of $ x $ .

The sum of all interior angles of the triangle is $ {180^ \circ } $ .

The angle of the straight line is $ {180^ \circ } $ .

**:**

__Complete step-by-step answer__Consider the given figure. Draw a straight line from a point D which bisects the line $ AB $ . Let name the point as E which bisects the line $ AB $ .

Using the property “the sum of all interior angles of a triangle is $ {180^ \circ } $ ”

Now consider the $ \vartriangle ACE $

The sum of all interior angles is,

$ {48^ \circ } + {30^ \circ } + a = {180^ \circ } $

$ \Rightarrow {78^ \circ } + a = {180^ \circ } $

$ \Rightarrow a = {180^ \circ } - {78^ \circ } $

$ \Rightarrow a = {102^ \circ } $

Therefore the $ \left| \!{\underline {\,

E \,}} \right. $ in the $ \vartriangle ACE $ is $ {102^ \circ } $ .

Now consider the straight line $ AB $ where E is the midpoint of $ AB $ . We know that the angle of the straight line is $ {180^ \circ } $ . We know value of the $ \left| \!{\underline {\,

{AEC} \,}} \right. $ is $ {102^ \circ } $ .

Therefore, we have $ \left| \!{\underline {\,

E \,}} \right. = \left| \!{\underline {\,

{AEC} \,}} \right. + \left| \!{\underline {\,

{CEB} \,}} \right. $

$ \Rightarrow \left| \!{\underline {\,

E \,}} \right. = {102^ \circ } + y $

$

\Rightarrow {180^ \circ } = {102^ \circ } + y \\

\Rightarrow y = {180^ \circ } - {102^ \circ } \;

$

$ \Rightarrow y = {78^ \circ } $

Now let us consider the $ \vartriangle DEB $

The sum of all interior angles is,

$ {40^ \circ } + {78^ \circ } + z = {180^ \circ } $

$ \Rightarrow {118^ \circ } + z = {180^ \circ } $

$ \Rightarrow z = {180^ \circ } - {118^ \circ } $

$ \Rightarrow z = {62^ \circ } $

Therefore $ \left| \!{\underline {\,

{EDB} \,}} \right. $ IS $ {62^ \circ } $ .

Now consider the straight line $ EC $ where D is the midpoint of $ EC $ . We know that the angle of the straight line is $ {180^ \circ } $ . We know value of the $ \left| \!{\underline {\,

{DEB} \,}} \right. $ is $ {62^ \circ } $ .

Therefore, we have $ \left| \!{\underline {\,

D \,}} \right. = \left| \!{\underline {\,

{EDB} \,}} \right. + \left| \!{\underline {\,

{CDB} \,}} \right. $

$ \Rightarrow \left| \!{\underline {\,

D \,}} \right. = {62^ \circ } + b $

$

\Rightarrow {180^ \circ } = {62^ \circ } + b \\

\Rightarrow b = {180^ \circ } - {62^ \circ } \;

$

$ \Rightarrow b = {118^ \circ } $

Therefore, the value of $ x $ is $ {118^ \circ } $ .

**So, the correct answer is “Option A”.**

**Note**: Candidates should be careful in determining the angles which are unknown. Here use these properties. The sum of all interior angles of the triangle is $ {180^ \circ } $ and the angle of the straight line is $ {180^ \circ } $ . Or we can use another property: the sum of interior angles is equal to the opposite exterior angle.

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

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

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

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