Question

in the adjoining figure PQ parallel to RS find X and Y

Answer 1

Using the properties of parallel lines we calculate the value of x as 40° and the value of y as 55° .

Given:

PQ||RS

The two angles are given: 25° , 30° and 60° .

To Find:

The value of the angle marked by x and y

Solution:

The complete diagram with relevant nomenclature is attached below.

From the properties of parallel lines, we know that the corresponding angles are equal.

So we consider the point of Intersection of the transversal with the parallel lines PQ and RS at points A and B respectively.

Now ∠PAB and ∠RBA are corresponding angles.

$\angle PAB=\angle RBC\\\\or, 25^{\circ}+y=65^{\circ}\\\\or, y = 40^{\circ}$

Thus the value of the angle marked by y is 40°.

Now the property of the co-interior angle states that:

$\angle PAB+\angle RBA=180^{\circ}\\\\or, \angle RBA = (180-65)^{\circ}\\\\or,\angle RBA = 115^{\circ}$

Now  $\angle OBA = (115-30)^{\circ} = 85^{\circ}$

In the ΔOAB we get :

$x+y+\angle OBA =180^{\circ}$ (angle sum property)

$or, 40+x+85 =180^{\circ}\\\\or, x=55^{\circ}$

Therefore the values of the angles x and y are 40° and 55° respectively as calculated using parallel lines.

To learn more about parallel lines visit:

https://brainly.in/question/1399334

https://brainly.in/question/1411186

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