Question

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

Answer 1

Let `∠`1 = 3x and `∠`2 = 2x

`∠`1and `∠`2 are linear pair of angle

Now,  `∠`1+ `∠`2 = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

x = `(180°)/5`

⇒ x = 36°

∴`∠`1 = 3x = 108°, `∠`2 = 2x = 72°

Vertically opposite angles are equal

`∠`1 = `∠`3 = 108°

`∠`2 = `∠`4 = 72°

`∠`6 = `∠`7 = 108°

`∠`5 = `∠`8 = 72°

Corresponding angles

`∠`1 = `∠`5 = 108°

`∠`2 = `∠`6 = 72°