Question

Plz answer fast with all steps

Answer 1

Step-by-step explanation:

Given :-

l || m , n is a transversal and x:y = 3:7

To find :-

Find the measures of x ,y and z ?

Solution :-

Given that

l || m

x:y = 3:7

Let x = 3k and y = 7k

From the figure

x and y forms a linear pair

=> x+y = 180°

=> 3k + 7k = 180°

=> 10k = 180°

=> k = 180°/10

=> k = 18°

Now,

x = 3k = 3×18° = 54°

y = 7k = 7×18° = 126°

and

l || m and n is a transversal

y and z are exterior angles on the same side to the transversal.

We know that

If two parallel lines Intersected by a transversal then the exterior angles on the same side to the transversal are supplementary.

=> y+z = 180°

=> 126° + z = 180°

=> z = 180°-126°

=> z = 54°

or

x and z are corresponding angles

We know that

If two parallel lines Intersected by a transversal then the corresponding angles to the transversal are equal.

=> x = z

=> z = 54°

Answer:-

The measure of x = 54°

The measure of y = 126°

The measure of z = 54°

Used formulae:-

→ If two parallel lines Intersected by a transversal then the corresponding angles to the transversal are equal.

→ If two parallel lines Intersected by a transversal then the exterior angles on the same side to the transversal are supplementary.

→ The sum of two adjacent angles is 180° then they are a linear pair.

Answer 2

Step-by-step explanation:

So let us consider x is =3x and y is 7x

X and y are in linear pair of angle,they will measure 180 degree

3x+7x =180

10x=180

x=180/10

x=18degree

3x will be equal to 3*18=54

7x will be equal to 7*18=126

y=126 degree

x=54

X and z are alternate angles so they will be congruent. Means same so,

Z=54 DEGREE

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