In Fig, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all

1.	In Fig, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.
Answer» Let, ∠1 = 3x ∠2 = 2x ∠1 + ∠2 = 180°(Linear pair) 3x + 2x = 180° 5x = 180° x = 36° Therefore, ∠1 = 3x = 108° ∠2 = 2x = 72° Vertically opposite angles are equal, so: ∠1 = ∠3 = 108° ∠2 = ∠4 = 72° ∠5 = ∠7 = 108° ∠6 = ∠8 = 72° Corresponding angles: ∠1 = ∠5 = 108° ∠2 = ∠6 = 72°

In Fig, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Answer»

Let, ∠1 = 3x

∠2 = 2x

∠1 + ∠2 = 180°(Linear pair)

3x + 2x = 180°

5x = 180°

x = 36°

Therefore,

∠1 = 3x = 108°

∠2 = 2x = 72°

Vertically opposite angles are equal, so:

∠1 = ∠3 = 108°

∠2 = ∠4 = 72°

∠5 = ∠7 = 108°

∠6 = ∠8 = 72°

Corresponding angles:

∠1 = ∠5 = 108°

∠2 = ∠6 = 72°