in the given figure, m parallel n and angle 1 and angle 2 are in the r

1.	in the given figure, m parallel n and angle 1 and angle 2 are in the ratio 4:5 Determine all the angles.
Answer» Answer :- The angles are ∠1 = 80°, ∠2 = 100°, ∠3 = 80°, ∠4 = 100°, ∠5 = 80°, ∠6 = 100°, ∠7 = 80° and ∠8 = 100°. Step-by-step explanation To FIND :- All the angles. [∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8] ★ Solution Given that, ∠1 and ∠2 are in the ratio of 4:5. m \|\| n Assumption Let us assume the given ratio angles as 4x and 5x. Therefore, 4x + 5x = 180° ⇒ 4x + 5x = 180 ⇒ 9x = 180 ⇒ x = 180/9 ⇒ x = 20 The value of x is 20. Hence, The angles are :- ⇒ ∠1 = 4x = 420 = 80° ⇒ ∠2 = 5x = 520 = 100° _________________________ Now, The angles are :- As given m \|\| n, ACCORDING the question, ➩ ∠3 = ∠1 = 80° ... opposite angle. ➩ ∠4 = ∠2 = 100° ... opposite angles. ➩ ∠5 = ∠3 = 80° ... alternate angles. ➩ ∠6 = ∠4 = 100° ... alternate angles. ➩ ∠7 = ∠1 = 100° ... EXTERIOR angles. ➩ ∠8 = ∠2 = 80° ... exterior angles.

in the given figure, m parallel n and angle 1 and angle 2 are in the ratio 4:5 Determine all the angles.

Answer»

Answer :-

The angles are ∠1 = 80°, ∠2 = 100°,

∠3 = 80°, ∠4 = 100°, ∠5 = 80°,

∠6 = 100°, ∠7 = 80° and ∠8 = 100°.

Step-by-step explanation

To FIND :-

All the angles.

[∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8]

★ Solution

Given that,

∠1 and ∠2 are in the ratio of 4:5.
m || n

Assumption

Let us assume the given ratio angles as 4x and 5x.

Therefore,

4x + 5x = 180°

⇒ 4x + 5x = 180

⇒ 9x = 180

⇒ x = 180/9

⇒ x = 20

The value of x is 20. Hence, The angles are :-

⇒ ∠1 = 4x = 4*20 = 80°

⇒ ∠2 = 5x = 5*20 = 100°

_________________________

Now, The angles are :-

As given m || n,

ACCORDING the question,

➩ ∠3 = ∠1 = 80° ... opposite angle.

➩ ∠4 = ∠2 = 100° ... opposite angles.

➩ ∠5 = ∠3 = 80° ... alternate angles.

➩ ∠6 = ∠4 = 100° ... alternate angles.

➩ ∠7 = ∠1 = 100° ... EXTERIOR angles.

➩ ∠8 = ∠2 = 80° ... exterior angles.