in the given figure, m parallel n and angle 1 and angle 2 are in the ratio 4:5 Determine all the angles.
Answers
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.
Step-by-step explanation:
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.