Question

In Fig 8.106, l, m and n are parallel lines intersected by transversal p at X, Y and and Z respectively. Find ∠1, ∠2 and∠3.

Answer 1

The values of the angles are $\angle 1=60^{\circ}$ , $\angle 2=120^{\circ}$ and $\angle 3=60^{\circ}$

Explanation:

Given that l,m and n are parallel lines intersected by transversal p at X, Y and Z.

We need to determine the values of the angles 1,2 and 3

The value of $\angle 3$ :

Since, the angle 3 and the nearest angle 120° lie on the straight line.

They are linear pair of angles. Hence, their angles add up to 180°

Thus, we have,

$\angle 3+120^{\circ}=180^{\circ}$

           $\angle 3=60^{\circ}$

Thus, the value of angle 3 is $\angle 3=60^{\circ}$

The value of $\angle 1$ :

Since, the lines l and m are parallel lines. And $\angle 3$ and $\angle 1$ are corresponding angles.

Since, we know that the corresponding angles are always equal.

Thus, we have,

$\angle 1=\angle 3$

$\angle 1=60^{\circ}$

Thus, the value of angle 1 is $\angle 1=60^{\circ}$

The value of $\angle 2$:

Since, the lines m and n are parallel lines. And the angles 2 and the angle containing 120° are alternate interior angles.

Since, we know that the alternate interior angles are always equal.

Thus, we have,

$\angle 2=120^{\circ}$

Hence, the value of angle 2 is $\angle 2=120^{\circ}$

Learn more:

(1) In figure l, m and n are Parallel Lines intersected by a transversal part X, Y and Z respectively

brainly.in/question/5429319

(2) In a figure,the parallel lines l and m are cut by a transversal n. If angle 1 and angle 2 are (5x-10)degree and (3x+60)degree respectively,then find the measures of angle 1 and angle 2.

brainly.in/question/1016807

Answer 2

Step-by-step explanation:

As per diagram,

l∣∣m∣∣n and p is transversal.

We know that 60

 and ∠4 angles on a straight line.

60+∠4=180

∴∠4=120  

  We know that corresponding angle are equal  

∠1=∠4    [ ∵ l∣∣m and p is transversal ]

∠1=∠2    [ ∵ m∣∣n and p is transversal ]

=> ∠1=∠4=120  

    [ ∵ ∠4=120]  

    ∠1=∠2=∠4=120  

   We know that vertically opposite angles are equal.

      ∠3=∠2  

=>  ∠3=120  

   [ ∵ ∠4=120  ]  

∴∠1=∠2=∠3=∠4=120