Two parallel lines l and m be cut by a transversal t, forming angles.
It is given that ∠1: ∠2 = 5: 7
Let the measures of angel be 5x and 7x,
Then,
5x + 7x = 180°
12x = 180°
x = 180/12
x = 15°
∴ ∠1 = 5x = 5 × 15 = 75°
∠2 = 7x = 7 × 15 = 105°
We know that,
∠2 + ∠3 = 180° … [∵ linear pair]
105° + ∠3 = 180°
= ∠3 = 180° – 105°
= ∠3 = 75°
∠3 + ∠6 = 180° … [∵ the sum of the consecutive interior angle is 180°]
75° + ∠6 = 180°
∠6 = 180 – 75
∠6 = 105°
Now ∠6 = ∠8 = 105° … [∵ vertically opposite angles are equal]
∴ ∠1= 75°, ∠2 = 105°, ∠3 = 75° and ∠8 = 105°.
