Question

Pls help me out in this question​

Answer 1

$<marquee>✌72°✌</marquee>$$\huge{\boxed{\red{\mathfrak{Answer}}}}$

Given,

l||m

a:b=2:3.

Let the angles be 2x and 3x.

Therefore,

a+b=180° [Linear pair]

2x+3x=180°

5x=180°

x=180/5

x=36°

Therefore,

a=72°

Now,

a=y [Alternate exterior angles]

Therefore,

y=72°.

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Answer 2

$\bigstar \underline{\bf\orange{Diagram:}}$

$\setlength{\unitlength}{20} \begin{picture}(7, 7) \put(3,3 ){\vector(1, 0){2.5}}\put(3,3 ){\vector( - 1,0 ){2.5}}\put(3, 1.5){\vector(1, 0){2.5}}\put(3,1.5){\vector( - 1,0 ){2.5}}\put(3,2 ){\vector( - 1,1 ){2}}\put(3, 2){\vector(1, - 1){2}}\qbezier(4.2, 1.5)(4.5, 1)(4, 1)\qbezier(1.25, 3)(1.5,3.25)(1.7,3.25 )\qbezier(2.5,3 )(2.5,3.5 )(1.7, 3.3)\put(5.5,3 ){ \tt l }\put(5.5,1.5 ){ \tt m }\put(4.3,0.9 ){ \tt y }\put(1, 4){ \tt n }\put(0.9, 3.25){ \tt a }\put(2.2,3.3 ){ \tt b }\put(5.3, 0.){\boxed{ \bf @Itz Archimedes }} \end{picture}$

$\bigstar\underline{\bf \green{Solution:}}$

Here ,

Line l has an angle of 180° . Since , it is a straight line and we have angle a & angle b on line l . Here , given angle a : angle b = 2 : 3

Let us assume angles a & b are part of x

Angle a : angle b = 2x : 3x

Now ,

$\to$ 2x + 3x = 180°

$\to$ 5x = 180°

$\to$ x = $\sf \dfrac{180}{5}$

$\to$ x = 36°

From the given figure

Angle a = Angle y

Since , angle a & y are alternate exterior & here we know that alternate exterior angles are always equal

Angle a = 2x

Substituting the value of x

Angle a = 2(36)

$\angle$ a = 72°

$\because \angle$a = 72° = $\angle$ y

$\bf\underline{Hence , \angle y=72^\circ}$