Question

answer the question ple​

Answer 1

$\pink{\pmb{ \sf{ \odot \:Question : }}}$

Find the value of x.

$\pink{\pmb{ \sf{ \odot \:Solution : }}}$

We can solve the following question with 2 methods :

• By first finding the adjacent angle to 110° and using angle sum property.
• Second method by using exterior angle property.

First Method :

Let the angle be y.

$\displaystyle{ \sf{\leadsto \: {110}^{ \circ} + y = {180}^{ \circ} \quad \: \quad(linear \: pair) }}$

$\displaystyle{ \sf{\leadsto \: y = {180}^{ \circ} - {110}^{ \circ} }}$

$\displaystyle{ \sf{\leadsto \: \pink{y= \bf{ {70}^{ \circ} }}}}$

Using angle sum property :

$\displaystyle{ \sf{\implies \: {50}^{ \circ} + y + x = {180}^{ \circ} }}$

Putting the value of y :

$\displaystyle{ \sf{\implies \: {50}^{ \circ} + {70}^{ \circ} + x = {180}^{ \circ} }}$

$\displaystyle{ \sf{\implies \: {120}^{ \circ} + x = {180}^{ \circ} }}$

$\displaystyle{ \sf{\implies \: x = {180}^{ \circ} - {120}^{ \circ} }}$

$\displaystyle{ \sf{\implies \: x = {60}^{ \circ} }}$

$\therefore \bf{Value \: of \: x \: is \: {60}^{ \circ}. }$

Method 2 :

The exterior angle property of the ∆ says that :

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Now by using this property,

$\displaystyle{ \sf{\leadsto \: {50}^{ \circ} + x = {110}^{ \circ} }}$

$\displaystyle{ \sf{\leadsto \: x = {110}^{ \circ} - {50}^{ \circ}}}$

$\displaystyle{ \sf{\leadsto \: \red{x = \bf{{60}^{ \circ} }}}}$

$\therefore \bf{Value \: of \: x \: is \: {60}^{ \circ}. }$

Conclusion :

$\pink{ \mathfrak{ \bigstar \: Value \: of \: x \: is \: {60}^{ \circ}. }}$