In Fig, AB ∥ CD and ∠1 and ∠2 are in the ratio of 3: 2. Determin

1.	In Fig, AB ∥ CD and ∠1 and ∠2 are in the ratio of 3: 2. Determine all angles from 1 to 8.
Answer» Given ∠1 and ∠2 are in the ratio 3: 2 Let us take the angles as 3x, 2x ∠1 and ∠2 are linear pair [from the figure] 3x + 2x = 180° 5x = 180° x = 180°/5 x = 36° Therefore, ∠1 = 3x = 3(36) = 108° ∠2 = 2x = 2(36) = 72° ∠1 and ∠5 are corresponding angles Therefore ∠1 = ∠5 Hence, ∠5 = 108° ∠2 and ∠6 are corresponding angles So ∠2 = ∠6 Therefore, ∠6 = 72° ∠4 and ∠6 are alternate pair of angles ∠4 = ∠6 = 72° Therefore, ∠4 = 72° ∠3 and ∠5 are alternate pair of angles ∠3 = ∠5 = 108° Therefore, ∠5 = 108° ∠2 and ∠8 are alternate exterior of angles ∠2 = ∠8 = 72° Therefore, ∠8 = 72° ∠1 and ∠7 are alternate exterior of angles ∠1 = ∠7 = 108° Therefore, ∠7 = 108° Hence, ∠1 = 108°, ∠2 = 72°, ∠3 = 108°, ∠4 = 72°, ∠5 = 108°, ∠6 = 72°, ∠7 = 108°, ∠8 = 72°

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

Answer»

Given ∠1 and ∠2 are in the ratio 3: 2

Let us take the angles as 3x, 2x

∠1 and ∠2 are linear pair [from the figure]

3x + 2x = 180°

5x = 180°

x = 180°/5

x = 36°

Therefore, ∠1 = 3x = 3(36) = 108°

∠2 = 2x = 2(36) = 72°

∠1 and ∠5 are corresponding angles

Therefore ∠1 = ∠5

Hence, ∠5 = 108°

∠2 and ∠6 are corresponding angles

So ∠2 = ∠6

Therefore, ∠6 = 72°

∠4 and ∠6 are alternate pair of angles

∠4 = ∠6 = 72°

Therefore, ∠4 = 72°

∠3 and ∠5 are alternate pair of angles

∠3 = ∠5 = 108°

Therefore, ∠5 = 108°

∠2 and ∠8 are alternate exterior of angles

∠2 = ∠8 = 72°

Therefore, ∠8 = 72°

∠1 and ∠7 are alternate exterior of angles

∠1 = ∠7 = 108°

Therefore, ∠7 = 108°

Hence, ∠1 = 108°, ∠2 = 72°, ∠3 = 108°, ∠4 = 72°, ∠5 = 108°, ∠6 = 72°, ∠7 = 108°, ∠8 = 72°