In the given figure, 1 || mand t is a transversal. I 41 and 22 are
in the ratio 5 : 7, find the measure of each of the angles
21, 22, 23 and 28.
Answers
Correct Question:-
In the given figure, l || m and t is a transversal. If ∠1 and ∠2 are in the ratio 5 : 7, find the measure of each of the angles ∠1, ∠2, ∠3 and ∠8.
Answer :-
Given:-
- l || m
- t is a transversal
- ∠1:∠2 = 5:7
To find :-
- ∠1, ∠2, ∠3 and ∠8.
Let the angles measure 5x and 7x. So , value of x is
⟹ ∠1+∠2 = 180° (linear pair)
⟹ 5x + 7x = 180
⟹ 12x = 180
⟹ x = 15
Putting the value in 5x & 7x which are ∠1 &∠2 respectively:-
⟹ ∠1 = 5x
= 5 (15)
= 75°
⟹ ∠2 = 7x
= 7(15)
= 105°
We know that ∠2 & ∠3 are linear pair so,
⟹ ∠2+∠3 = 180° (linear pair)
∠3 = 180−105
∠3 = 75°
And we also know that interior angles on the same side of the transversal are supplementary ; so ∠6 is :-
⟹ ∠3+∠6 = 180
∠6 = 180−∠3
∠6 = 105°
Angle 6 and Angle 8 are vertically opposite angle ; so
⟹∠6 =∠8
∠8 =105°
So , all angles are
∠1 = 75°
∠2 = 105°
∠3 = 75°
∠8 = 105°