Question

In the given figure L||M and M||N If x:y=3 : 2 then the value of z is:

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Answer 1

Answer:

The correct answer is

72

Concept

An angle is created when two straight lines or rays meet at a standard endpoint. The common point of contact is named the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.” Parts of Angles: Vertex, Arms, Initial Side and Terminal Side. interior angles: Interior Angles are the angles formed within or inside a shape. Exterior angles: Exterior angles are the angles formed outside a shape, between any side of a shape and an extended adjacent side.

Given

L||M

M||N

x:y=3 : 2

To find:

value of z

Step-by-step explanation:

Let x=3a and y=2a

Now y+ angle 1=180

 (Angle made on straight line (n) are supplementary)

2a+angle 1=180

1=180 −2a..........(i)

Now m∣∣n and t is transversal

x= angle 1   (Corresponding angles)

3a= angle 1

3a=180 - 2a

5a=180

a=36

Now y=2a=2*36=72

Now l∣∣n and t is transversal.

z=y =72

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Answer 2

Answer:

the value of z = 72°

Step-by-step explanation:

It is given to us that :

l || m and m || n = l || m || n

and x : y = 3 : 2

So, let the angles x and y be 3c and 2c respectively.

As a straight line cuts the parallel lines into three halves, hence

all angles on a straight line  = 180°

let the angle below the parallel line be 'd'

so, angle d  + angle y = 180°

or, angle d = 180° - angle y = 180° - 2c ......... eq(1)

now, angle d and angle x are corresponding angles

so, angle d = angle x

or, 180° - 2c = 3c

or, 180° = 5c

or, c = 36°

therefore, angle x = 3c = 3 x 36 = 108°

and angle y = 2c = 2 x 36 = 72°

now we can clearly see that angle y and angle z are corresponding angles

So, angle y = angle z = 72°

Hence, the value of z = 72°

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