Question

Solve the Question.

(Provided In Attachment).

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Answer 1

Answer:

x=60 (in degrees)

Step-by-step explanation:

Since l ∥ m, then

3y=2y+25 [Alternate ∠s]

⇒3y−2y=25

⇒y=25 ......(1)

Also x+15=2y+25 [Vertically opposite ∠s]

⇒x+15=2(25)+25 [using (1)]

⇒x+15=50+25

⇒x=75−15

⇒x=60 (in degrees) (Ans)

Answer 2

♕ $\large{ \rm{\gray{\underline{\underline { \red{S} \purple{O} \pink{LU} \orange{TI} \green{ON}}}}}}$ ♕

$\pink{ \rm{Given :-}}$

l is parallel to m ( l || m )

$\pink{ \rm{To \: Find :-}}$

The value of x.

$\pink{ \rm{Let's \: Find \: Out :-}}$

Here,

❍ $\small{ \sf{3y° = 2y° + 25°}}$ (Alternate interior angles are equal)

◑ $\small{ \rm{ 3y° - 2y° = 25°}}$

◑ $\small{ \rm{y = 25°}}$

Now, find the value of x :-

❍ $\small{ \rm {2y° + 25° = x + 15 }}$ (Vertically Opposite angles are equal)

Now, Substituting the value of y.

◑ ${ \small{ \rm{2(25°) + 25° = x + 15°}}}$

◑ ${ \small{ \rm{50° + 25° = x + 15°}}}$

◑ $\small{ \rm{x = 50° + 25° - 15°}}$

◑ $\boxed{ \rm{ \gray{x = 60°}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\rm{ \purple{Assimilate \: It :-}}$

• The angles which are formed between the two parallel lines and on the opposite sides of transversal are called alternate interior angles or alternate angles.

• Alternate interior angles are equal.

• A straight line that intersects two or more straight lines in a plane at different points is called transversal.

• When two straight lines intersect each other, then they form four angles at their points of intersection. These angles are called Vertically opposite angles.

• Vertically opposite angles are equal.